{"id":45,"date":"2023-09-17T10:55:22","date_gmt":"2023-09-17T10:55:22","guid":{"rendered":"https:\/\/mathority.org\/id\/titik-belok-suatu-fungsi\/"},"modified":"2023-09-17T10:55:22","modified_gmt":"2023-09-17T10:55:22","slug":"titik-belok-suatu-fungsi","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/titik-belok-suatu-fungsi\/","title":{"rendered":"Titik belok suatu fungsi"},"content":{"rendered":"<p>Berikut kami jelaskan apa itu titik belok suatu fungsi dan cara mencari semua titik belok suatu fungsi. Selain itu, Anda akan menemukan latihan langkah demi langkah tentang kelengkungan dan titik belok suatu fungsi. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-puntos-de-inflexion-de-una-funcion\"><\/span> Apa titik belok suatu fungsi?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Titik belok suatu fungsi adalah titik dimana grafik fungsi tersebut mengalami perubahan kelengkungan, yaitu pada suatu titik belok suatu fungsi berubah dari cekung menjadi cembung atau sebaliknya.<\/strong> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-saber-si-una-funcion-tiene-un-punto-de-inflexion\"><\/span> Bagaimana cara mengetahui apakah suatu fungsi mempunyai titik belok<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dengan mengetahui definisi titik belok, mari kita lihat cara mengetahui apakah suatu titik tertentu merupakan titik belok suatu fungsi. <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 35px; padding-left: 30px; border-radius:30px;\">\n<p> Suatu fungsi mempunyai <strong>titik belok<\/strong> di titik-titik yang menghilangkan turunan keduanya dan turunan ketiganya bukan nol.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0deb5fc13e20049e642bdc68a5c35a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l}f''(a)=0\\\\[2ex]f'''(a)\\neq 0\\end{array}\\right\\} \\quad \\bm{\\longrightarrow} \\quad x=a \\text{ es un punto de inflexi\\'on}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"405\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p> Sebagai contoh, kita akan menghitung titik belok fungsi derajat ketiga berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37bed97da1ec1d3c4eefd018c3d75650_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-5x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama, kita menghitung turunan kedua dan ketiga dari fungsi tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-379ab2238c65191bfc16a940f5a7375d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86d5e98dcde33659284eaafb55050852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=6x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d65ebc63b5e7fa667d5e25e40448942c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'''(x)=6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang kita atur turunan keduanya sama dengan 0 dan selesaikan persamaan yang dihasilkan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7878c5d5f08c25729d37b94ea643bdf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Maka titik x=0 akan menjadi titik belok fungsi tersebut jika turunan ketiganya bukan nol pada titik tersebut. Dalam kasus kita, turunan ketiga selalu sama dengan 6.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e11c7a68a7805dd5d27f43c4d332d11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'''(0)=6\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, x=0 adalah titik belok dari fungsi tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-estudiar-la-curvatura-y-hallar-los-puntos-de-inflexion-de-una-funcion\"><\/span> Cara mempelajari kelengkungan dan mencari titik belok suatu fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita baru saja melihat metode untuk menemukan titik balik. Namun, kita biasanya cenderung mempelajari kelengkungan suatu fungsi, yaitu menentukan kecekungan dan kecembungan suatu fungsi, dan dari sana menghitung titik beloknya.<\/p>\n<p> Untuk mencari titik belok suatu fungsi melalui kelengkungannya, perlu dilakukan langkah-langkah sebagai berikut: <\/p>\n<div style=\"background-color:#FFF3E0; padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 10px; border-radius:30px;\">\n<ol style=\"color:#64B5F6; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Temukan <strong>titik-titik yang tidak termasuk dalam domain<\/strong> fungsi tersebut.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Hitung turunan pertama dan <strong>turunan kedua fungsi tersebut.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Temukan <strong>akar-akar turunan kedua<\/strong> , yaitu menghitung titik-titik yang menghilangkan turunan kedua dengan menyelesaikannya\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> .<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Buatlah <strong>interval<\/strong> dengan akar-akar turunan dan titik-titik yang tidak termasuk dalam domain fungsi tersebut.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Hitung nilai turunan kedua pada suatu titik pada setiap interval.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Tanda turunan kedua<\/strong> menentukan kecekungan atau kecembungan suatu fungsi pada interval ini:<\/span>\n<ul style=\"color:#64B5F6; font-weight: bold; margin-top:8px; margin-left:8%\">\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">Jika turunan kedua dari fungsi tersebut positif, maka fungsi tersebut <strong>cembung<\/strong> pada interval tersebut.<\/span><\/li>\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">Jika turunan kedua dari fungsi tersebut negatif, maka fungsi tersebut <strong>cekung<\/strong> pada interval tersebut.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Titik belok<\/strong> adalah titik dimana fungsi berubah dari cembung ke cekung atau sebaliknya.<\/span><\/li>\n<\/ol>\n<\/div>\n<p> Agar Anda dapat melihat bagaimana titik belok suatu fungsi dihitung menggunakan prosedur ini, kami akan menyelesaikan contoh langkah demi langkah di bawah ini:<\/p>\n<ul>\n<li> Pelajari kelengkungan dan temukan titik belok dari fungsi polinomial berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1c8c498c40649602a0573f686b30f46d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4-6x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Hal pertama yang harus dilakukan adalah menghitung domain definisi fungsi. Ini adalah fungsi polinomial, sehingga domain dari fungsi tersebut terdiri dari bilangan real, artinya fungsi kontinu:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Setelah kita menghitung domain dari fungsi tersebut, kita perlu mempelajari pada titik mana fungsi tersebut terpenuhi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> .<\/p>\n<p> Oleh karena itu, pertama-tama kita menghitung turunan pertama dari fungsi tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7602daac91808a70b1b980676921f6d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^4-6x^2 \\ \\longrightarrow \\ f'(x)= 4x^3-12x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"314\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Selanjutnya, kita menghitung turunan kedua dari fungsi tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-53a801c5309b20a5ad6b5b5981fde19e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=4x^3-12x \\ \\longrightarrow \\ f''(x)= 12x^2-12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita menetapkan turunan kedua sama dengan 0 dan menyelesaikan persamaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ce944968a13592d994b5d76185e2ae9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^2-12=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"107\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5db8208512c91e36a1ece605a967be0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12x^2=12\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22930ba9e08e00b2388ec1a767443147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=\\cfrac{12}{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"61\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-959000af33497314f9a59a9bed2a19c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-003a71cb0ec797dfcd0cca915b03a795_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=\\sqrt{1}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa2841908f61047e2edf3a8b60ab5962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Setelah kita menghitung domain dari fungsi dan<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-981d85a257dd56afdb3fc7eb53d5eadf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<p> , kami mewakili semua titik kritis yang terdapat pada garis bilangan: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nombre-ligne-1-1.webp\" alt=\"\" class=\"wp-image-2596\" width=\"312\" height=\"79\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Dan sekarang kita evaluasi tanda turunan keduanya pada setiap interval, untuk mengetahui apakah fungsinya cekung atau cembung. Oleh karena itu, kita mengambil sebuah titik pada setiap interval (tidak pernah titik kritisnya) dan melihat tanda apa yang dimiliki turunan kedua pada titik tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3268d2c9fa6d3192f84d914bb9163680_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=12x^2-12\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"141\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-290ddf1ed5524d38fa79c593052cca0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-2) = 12\\cdot (-2)^2-12 =36 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"287\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc8cd9fb09f76eeb69fdeda81a49c674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0) = 12\\cdot 0^2-12 = -12 \\  \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f35d5dc33f0ffbdf9b02b856ff70e1fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2) = 12\\cdot 2^2-12=36 \\  \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"245\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-1-1-positif-negatif-positif.webp\" alt=\"\" class=\"wp-image-2597\" width=\"315\" height=\"140\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Jika turunan keduanya positif berarti fungsinya cembung.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , dan jika turunan keduanya negatif berarti fungsinya cekung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, interval kecekungan dan kecembungan fungsi tersebut adalah:<\/p>\n<p class=\"has-text-align-center\"> <strong>Cembung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9f11bddd110e2869bf60761b066d16c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-1) \\cup (1,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>Cekung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c8937d362a3ba07fa9068381afe74a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Selanjutnya pada x=-1 fungsinya berubah dari cembung menjadi cekung, sehingga <strong>x=-1 merupakan titik belok<\/strong> dari fungsi tersebut <strong>.<\/strong> Dan pada x=1, fungsinya berubah dari cekung menjadi cembung, jadi <strong>x=1 juga merupakan titik belok<\/strong> fungsi tersebut.<\/p>\n<p> Terakhir, kita substitusikan titik-titik yang ditemukan ke dalam fungsi asli untuk mencari koordinat Y dari titik belok:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da3f60ecfa8eb1666821a1a26a103825_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=(-1)^4-6(-1)^2 = 1-6 \\cdot 1 = -5 \\ \\longrightarrow \\ (-1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"437\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8544d4624c7030bd065734e22efd792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^4-6\\cdot 1^2 = 1-6 \\cdot 1 = -5 \\ \\longrightarrow \\ (1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"367\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, titik balik dari fungsi tersebut adalah:<\/p>\n<p class=\"has-text-align-center\"> <strong>Titik balik:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2576ee14a4d19421150e7b696f83c31f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-1,-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>Dan<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2220ee8c6ddd44fd21975caeace894d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(1,-5)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Di bawah ini Anda dapat melihat representasi grafis dari fungsi yang dipelajari: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/points-dinflexion-dune-fonction.webp\" alt=\"titik belok suatu fungsi\" class=\"wp-image-2598\" width=\"457\" height=\"493\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Seperti yang Anda lihat dari grafik, fungsinya berubah dari cembung<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2bb599fff4b55075f6de7628a35f822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> menjadi cekung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69b1c740acf744d34bf12f12dedabf65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cap)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> Tentang<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1bf0660982e8c9a229e9bd39f6a71341_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> karena kelengkungannya berubah. Di sisi lain, fungsinya beralih dari cekung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69b1c740acf744d34bf12f12dedabf65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cap)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> menjadi cembung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2bb599fff4b55075f6de7628a35f822_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\cup)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> Tentang<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97e5c7dfce41ba68b73f6246d1554039_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<p> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-puntos-de-inflexion\"><\/span> Latihan memutar yang terpecahkan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung interval kecekungan dan kecembungan serta titik belok fungsi eksponensial berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-175df6eaf87d8a34e6c7f52ffcf4dde7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Hal pertama yang harus dilakukan adalah menghitung domain definisi fungsi. Fungsi tersebut terdiri dari fungsi polinomial (x) yang domainnya hanya terdiri dari bilangan real, dan fungsi eksponensial ( <sup>ex<\/sup> ), yang domainnya juga terdiri dari bilangan real. Oleh karena itu, domain dari fungsi tersebut terdiri dari bilangan real:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f565027fd5d2a4381e3a23d183c9f76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita hitung turunan dari fungsi tersebut. Dalam hal ini, fungsi tersebut terdiri dari hasil kali dua fungsi, jadi untuk menurunkan fungsi tersebut kita perlu menerapkan rumus turunan suatu hasil kali: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-996eb43fbe77816d37d7bfa7f35e1e63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=1 \\cdot e^x+ x \\cdot e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3d95f44577d8448674370dd53e02726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=e^x +xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Selanjutnya, kita menghitung turunan kedua dari fungsi tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-956f25a80e8ccc50a8888c8adc1e134e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= e^x + 1 \\cdot e^x+ x \\cdot e^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-551f7a75a4b0338b53e7decaf413e976_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)=e^x +e^x + xe^x  = 2e^x +xe^x\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"267\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menetapkan turunan kedua sama dengan 0 dan menyelesaikan persamaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc9977afe23305adab3b6c332e4232bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2e^x+xe^x= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"107\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami mengekstrak faktor persekutuan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf04b8cea9a81435b3106d94a8bba193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^x(2+x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agar perkaliannya sama dengan 0, salah satu dari dua unsur perkaliannya harus nol. Oleh karena itu, kami menetapkan setiap faktor sama dengan 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4b369d45e5559de1f7069b49db2d173_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle e^x\\cdot(2+x) =0 \\longrightarrow \\begin{cases} e^x=0 \\ \\color{red}\\bm{\\times}\\color{black}  \\\\[2ex] 2+x=0 \\ \\longrightarrow \\ x= - 2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"350\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Suatu bilangan yang dipangkatkan ke bilangan lain tidak akan pernah menghasilkan 0. Oleh karena itu, persamaannya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0108040ee23df4da2db681c9ffb2decc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e^x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> Tidak ada solusi.<\/p>\n<p class=\"has-text-align-left\"> Kami mewakili semua titik tunggal yang diperoleh di sebelah kanan: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-2-1.webp\" alt=\"\" class=\"wp-image-2602\" width=\"199\" height=\"78\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Dan sekarang kita evaluasi tanda turunan keduanya pada setiap interval untuk mengetahui apakah fungsinya cekung atau cembung. Untuk melakukan ini, kita mengambil sebuah titik di setiap interval dan melihat tanda mana yang memiliki turunan kedua di titik tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5deb7fd9574dd41f2571836c131654d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-3)= 2e^{-3} +(-3)\\cdot e^{-3} = 0,1 - 0,15 = -0,05\\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"442\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc38d25b16bf677962f89d5562265437_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(0)= 2e^0 +0\\cdot e^0 = 2 \\cdot 1 + 0 \\cdot 1 =2+0= 2 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-2-courbure.webp\" alt=\"\" class=\"wp-image-2603\" width=\"201\" height=\"135\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Jika turunan keduanya positif berarti fungsinya cembung.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , dan jika turunan keduanya negatif berarti fungsinya cekung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, interval kecekungan dan kecembungan adalah:<\/p>\n<p class=\"has-text-align-center\"> <strong>Cembung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-087de0300a010f86265ccd4f69d8570e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>Cekung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-266c9537df2a55b66ad1c2868728fddf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Selain itu, fungsi berubah dari cekung menjadi cembung pada x=-2, jadi <strong>x=-2 adalah titik belok<\/strong> fungsi tersebut.<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kita substitusikan titik belok yang ditemukan ke dalam fungsi asli untuk mencari koordinat Y dari titik tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3aee30bfafb6ab70bdc2bc672a61a780_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2) = (-2)\\cdot e^{-2} =-2e^{-2} \\ \\longrightarrow \\ (-2,-2e^{-2})\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"362\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kesimpulannya, satu-satunya titik balik dari fungsi ini adalah:<\/p>\n<p class=\"has-text-align-center\"> <strong>Titik balik:<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-676ef444bb4f5ed3116dc104f451295d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,-2e^{-2})}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Pelajari interval kecekungan dan konveksitas dan temukan titik belok dari fungsi rasional berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ac9ccc5e8540cca38f599ed36507792_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x^3}{x^2-4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"109\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama kita perlu menghitung domain dari fungsi tersebut. Karena ini adalah fungsi rasional, kita menetapkan penyebutnya sama dengan nol untuk melihat bilangan mana yang tidak termasuk dalam domain fungsi tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a34dfe78d673534873a2013c16e1b353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-4= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c269e23a1070b3e5556abece040af75a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4c32359b264b28ac80f2606c09d5a2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{x^2}=\\sqrt{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c06a55e3acdd1e283973786926b27716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Artinya jika x adalah -2 atau +2, penyebutnya adalah 0. Oleh karena itu, fungsinya tidak akan ada. Oleh karena itu, domain fungsi tersebut terdiri dari semua bilangan kecuali x=-2 dan x=+2.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e666f828709575f965b5120fbdda085e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f= \\mathbb{R}-\\{-2, +2 \\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kedua, kita menghitung turunan pertama dari fungsi tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1397d0e8e73bd7b1d851411dee28daed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{x^3}{x^2-4}  \\ \\longrightarrow \\ f'(x)= \\cfrac{3x^2 \\cdot (x^2-4) - x^3 \\cdot 2x }{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"396\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-495f08a881718b2734ef1db17b5f39ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)= \\cfrac{3x^4-12x^2-2x^4}{\\left(x^2-4\\right)^2} = \\cfrac{x^4-12x^2}{\\left(x^2-4\\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"298\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Lalu kita selesaikan turunan keduanya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50df15bb48cacf8f031b640994661e47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 2\\left(x^2-4\\right)\\cdot 2x }{ \\left(\\left(x^2-4\\right)^2 \\right)^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"483\" style=\"vertical-align: -33px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b05b5f09c2adbfead593df2cdf2ad29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^2 - \\left(x^4-12x^2\\right)\\cdot 4x\\left(x^2-4\\right) }{\\left(x^2-4\\right)^4 }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"461\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Semua suku dikalikan dengan<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1e0f0d9a63183e28c50a5cedcddeddd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x^2-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu kita dapat menyederhanakan pecahan tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92e1aa280d06bf8b58045845d5e21f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right)^{\\cancel{2}} - \\left(x^4-12x^2\\right)\\cdot 4x\\cancel{\\left(x^2-4\\right)} }{\\left(x^2-4\\right)^{\\cancelto{3}{4}} }\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"458\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a912eff3359969b6ffbef96a3f16932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{\\left(4x^3-24x\\right)\\cdot \\left(x^2-4\\right) - \\left(x^4-12x^2\\right)\\cdot 4x}{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"386\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8bc35bdd2b70bbac52fa0f24bbefa261_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - \\left(4x^5-48x^3\\right) }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"381\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-045971f71cc11ced77ea0df9f2c514fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{4x^5-16x^3-24x^3+96x - 4x^5+48x^3 }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"365\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3144a0aa00ee8ec427752f05f0fac40c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= \\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"145\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang mari kita hitung akar-akar turunan kedua dari fungsi tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f618f4961c18c45be60fc496ad4896e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(x)= 0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8ed519add27a4d51c75b49179e632ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{8x^3+96x  }{\\left(x^2-4\\right)^3 }=0\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"109\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Syarat<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8590a90fab5aef55d7b45cd89e01943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"70\" style=\"vertical-align: -7px;\"><\/p>\n<p> Caranya adalah dengan membagi seluruh ruas kiri, sehingga kita dapat mengalikannya dengan seluruh ruas kanan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b5c0d1e44accc3b68a67598f5c4d834c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\\cdot \\left(x^2-4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"193\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c52a7448e4acc67488ef5747cc3bed9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3+96x =0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami mengekstrak faktor persekutuan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f2884a1c9b8dabf6ea5323f2ac71b2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x(8x^2+96)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agar perkaliannya sama dengan 0, salah satu dari dua unsur perkaliannya harus nol. Oleh karena itu, kami menetapkan setiap faktor sama dengan 0:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-31adba554b44aa92fd7227506440ccaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x\\cdot(8x^2+96) =0 \\longrightarrow \\begin{cases} \\bm{x =0} \\\\[2ex] 8x^2+96=0 \\ \\longrightarrow \\ x^2=\\cfrac{-96}{8}} = -12 \\ \\longrightarrow \\ x= \\sqrt{-12} \\ \\color{red}\\bm{\\times} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"635\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-635e2ffa452a5a66a4bcacb0e111c5ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= \\sqrt{-12}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"81\" style=\"vertical-align: -3px;\"><\/p>\n<p> Tidak ada penyelesaian karena tidak ada akar negatif dari bilangan real.<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita nyatakan pada garis semua titik kritis yang diperoleh, yaitu titik-titik yang tidak termasuk dalam domain (x=-2 dan x=+2) dan titik-titik yang membatalkan turunan kedua (x=0): <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droite-numerique-2-0-2.webp\" alt=\"\" class=\"wp-image-2399\" width=\"385\" height=\"75\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Dan kita evaluasi tanda turunan keduanya pada setiap interval, untuk mengetahui apakah fungsinya cekung atau cembung. Jadi kita ambil sebuah titik di setiap interval dan lihat tanda apa yang mempunyai turunan kedua di titik tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b5618d1ab96a078d50507f45155595b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-3)=\\cfrac{8(-3)^3+96(-3)  }{\\left((-3)^2-4\\right)^3 } = \\cfrac{-504}{125}=-4,03 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"408\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2e868f1f815d4155a187c55b004cc13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(-1)=\\cfrac{8(-1)^3+96(-1)  }{\\left((-1)^2-4\\right)^3 } = \\cfrac{-104}{-27}=3,85 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"394\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3814746f7f9e8aa3920e3f84cd0ff0eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(1)=\\cfrac{8\\cdot1^3+96\\cdot 1  }{\\left(1^2-4\\right)^3 } = \\cfrac{104}{-27}=-3,85 \\ \\rightarrow \\ \\bm{-}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"348\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54d98824f72954de12bc065471a610e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(3)=\\cfrac{8\\cdot 3^3+96\\cdot 3  }{\\left(3^2-4\\right)^3 } = \\cfrac{504}{125}=4,03 \\ \\rightarrow \\ \\bm{+}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"329\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/ligne-numerique-2-0-2-courbure.webp\" alt=\"\" class=\"wp-image-2568\" width=\"383\" height=\"129\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> Jika turunan keduanya positif berarti fungsinya cembung.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> , dan jika turunan keduanya negatif berarti fungsinya cekung<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, interval kecekungan dan kecembungan adalah:<\/p>\n<p class=\"has-text-align-center\"> <strong>Cembung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49efa6d9ab88562f20df743cb7d267f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cup})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0cd739761b2dc845594c0a0696a240c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-2,0)\\cup (2,+\\infty)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"> <strong>Cekung<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59e636042d77445b1534260d9d7309a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\bm{\\cap})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"24\" style=\"vertical-align: -5px;\"><\/p>\n<p> <strong>:<\/strong><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5e741ac026627200772655094f921f26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(-\\infty,-2)\\cup (0,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Fungsi tersebut mengubah kelengkungan di tiga titik, sehingga fungsi rasional pada prinsipnya mempunyai tiga titik belok, yaitu x=-2, x=0 dan x=2. Namun meskipun terjadi perubahan kelengkungan pada x=-2 dan x=+2, hal tersebut bukanlah titik belok karena tidak termasuk dalam domain fungsi. Sebaliknya, pada x=0 terjadi perubahan kelengkungan dan hal ini termasuk dalam fungsi tersebut, jadi <strong>x=0 adalah satu-satunya titik belok fungsi tersebut.<\/strong><\/p>\n<p class=\"has-text-align-left\"> Yang tersisa hanyalah menghitung koordinat Y dari titik belok:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba8c4d5b9201e0971f4a036ea6b0f887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(0)=\\frac{0^3}{0^2-4} =\\frac{0}{-4}=0\\ \\longrightarrow \\ (0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"279\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Singkatnya, satu-satunya titik belok fungsi rasional adalah titik asal koordinat:<\/p>\n<p class=\"has-text-align-center\"> <strong>Titik balik:<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c790019bd70403eba876c59c82c0f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(0,0)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Kita tahu itu fungsinya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a047814c11fd2f3da04a21a9d489da58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3+ax^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<p> melewati titik tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1542b88e9f0c10166380ce26011f4d14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<p> , memiliki nilai yang relatif ekstrim<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> , dan titik balik<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3976ff8b81cbf5060581dc2ccd19c5c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> . Dari informasi ini, hitung nilai parameter<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0357ced152d91599aefcf60b48861b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a, b\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> . <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Biarkan fungsi tersebut memiliki titik belok di<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a9b760ebc3dca7954a7b6656a30c8cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> maksudnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9c643154cd44808d027e645761f5921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f''(2)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, kita menghitung turunan kedua dari fungsi tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2a9b760ebc3dca7954a7b6656a30c8cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan kami menetapkannya sama dengan 0: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a452ebc56e45c70455952e82f24bc213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x) = x^3+ax^2+bx+c \\ \\longrightarrow \\  f'(x)=3x^2+2ax+b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"413\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88269f2eaaf1326ed88cec634a839505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(x)=3x^2+2ax+b \\ \\longrightarrow \\ f''(x)= 6x+2a\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"344\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-428d0d2aa58a4f0bee3155e72060aee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f''(2)=6\\cdot 2+2a\\\\[2ex] f''(2)=0\\end{array} \\right\\} \\longrightarrow 6\\cdot 2+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"301\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita selesaikan persamaan yang diperoleh untuk mencari nilai parameter a: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-08eaf911dd0de580da1db41c3a8a25d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6\\cdot 2+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"103\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4127c25ec4efd2c7b05070600fca7040_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"12+2a=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"89\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21de66a92427317edcb4a2475fcbb3f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2a=-12\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-313aff06eefaaf9af361841519334293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=\\cfrac{-12}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-81f76a9a366a0e75d702129c2a0cf565_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=-6}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsinya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f82d6e87e465fabd9889eec2ed94b7ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3+ax^2+bx+c \\ \\xrightarrow{a \\ = \\ -6}\\ f(x)=x^3-6x^2+bx+c\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Selain itu, fungsinya juga sangat ekstrim<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a0a069e4bb53cf46ff9611c104b13f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> , Artinya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba772a3114b7ee64171db5cc258b34b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, kita menghitung turunan pertama dari fungsi tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a0a069e4bb53cf46ff9611c104b13f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan kami menetapkannya sama dengan 0: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-347dc6fd1ded234104fd25f2e787c4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+bx+c \\ \\longrightarrow \\ f'(x)=3x^2-12x+b\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"412\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-561b9c2aa6ba34d90df560c5a97e3a92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f'(1)=3\\cdot 1^2-12\\cdot 1+b\\\\[2ex] f'(1)=0\\end{array} \\right\\} \\longrightarrow 3\\cdot 1^2-12\\cdot 1+b=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita selesaikan persamaan yang diperoleh untuk mencari nilai b yang tidak diketahui: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3362d7ea7f2e10163031aaa7ed824c52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3\\cdot 1^2-12\\cdot 1+b=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"161\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e6fe2c6a93ee7e3cda9732cced98c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3 \\cdot 1 -12 + b = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"132\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a73022570e08c83b3c148066c88595fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3 -12 + b = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"110\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cb3fc18020c592a99e0d3db8a57955f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b=+12-3\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"93\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a73ce8b725442e911ac1a46aceb20457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{b=9}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsinya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a7549d54df3579050c71e4e06eeb053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+bx+c \\ \\xrightarrow{b \\ = \\ 9} \\ f(x)=x^3-6x^2+9x+c\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"455\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Di sisi lain, mereka memberi tahu kita bahwa fungsi tersebut melalui titik (3,1). Artinya,<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-27c6a831fde145aea6f8d30359e84f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Oleh karena itu, kita dapat menerapkan kondisi ini untuk mencari nilai parameter c:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b496beb319ccab8292181ec1387ba9f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} f(3)=3^3-6\\cdot 3^2+9\\cdot3+c \\\\[2ex] f(3)=1 \\end{array} \\right\\} \\longrightarrow 3^3-6\\cdot 3^2+9\\cdot 3+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"467\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami menyelesaikan persamaan yang diperoleh untuk menemukan nilai <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4586bc1b16791cf732fc00ee37db4357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-410da829676625edf3c06a986ce96acb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3^3-6\\cdot 3^2+9\\cdot 3+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"190\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f860f41d277c58f8714e45bda45c1a27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-6\\cdot 9+27+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"170\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74e9b29b4c5de8c37cad4b293f196fca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27-54+27+c = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"157\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41daca67d3a063fdd50d16d2a3e43bb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c=1-27+54-27\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5825f757c3f04143a8c5598e0468cb33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{c=1}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsinya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd400bd7ca4f75d8ae12b7aa9e9680ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^3-6x^2+9x+c \\ \\xrightarrow{c \\ = \\ 1} \\ f(x)=x^3-6x^2+9x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"457\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Berikut kami jelaskan apa itu titik belok suatu fungsi dan cara mencari semua titik belok suatu fungsi. Selain itu, Anda akan menemukan latihan langkah demi langkah tentang kelengkungan dan titik belok suatu fungsi. Apa titik belok suatu fungsi? Titik belok suatu fungsi adalah titik dimana grafik fungsi tersebut mengalami perubahan kelengkungan, yaitu pada suatu titik &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/titik-belok-suatu-fungsi\/\"> <span class=\"screen-reader-text\">Titik belok suatu fungsi<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[49],"tags":[],"class_list":["post-45","post","type-post","status-publish","format-standard","hentry","category-representasi-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Titik belok suatu fungsi -<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/titik-belok-suatu-fungsi\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Titik belok suatu fungsi -\" \/>\n<meta property=\"og:description\" content=\"Berikut kami jelaskan apa itu titik belok suatu fungsi dan cara mencari semua titik belok suatu fungsi. Selain itu, Anda akan menemukan latihan langkah demi langkah tentang kelengkungan dan titik belok suatu fungsi. Apa titik belok suatu fungsi? 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