{"id":42,"date":"2023-09-17T10:58:59","date_gmt":"2023-09-17T10:58:59","guid":{"rendered":"https:\/\/mathority.org\/it\/equazione-tangente\/"},"modified":"2023-09-17T10:58:59","modified_gmt":"2023-09-17T10:58:59","slug":"equazione-tangente","status":"publish","type":"post","link":"https:\/\/mathority.org\/it\/equazione-tangente\/","title":{"rendered":"Equazione della retta tangente"},"content":{"rendered":"<p>In questo articolo vedremo <strong>come trovare l&#8217;equazione della tangente<\/strong> ad una curva. Inoltre, puoi allenarti con esercizi risolti di diversi livelli di difficolt\u00e0. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-la-recta-tangente-a-una-funcion-en-un-punto\"><\/span> Equazione della retta tangente ad una funzione in un punto <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> L&#8217; <strong>equazione della tangente<\/strong> alla funzione f(x) nel punto x=x <sub>0<\/sub> \u00e8:<\/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-326424811181144df35c0b94ce50c462_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -y_0= m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p align=\"LEFT\"> Dove il punto P(x <sub>0<\/sub> ,y <sub>0<\/sub> ) \u00e8 il punto in cui la tangente e la funzione coincidono. E la pendenza della tangente, m, \u00e8 uguale alla derivata della curva nel punto x <sub>0<\/sub> , cio\u00e8 m=f'(x <sub>0<\/sub> ). <\/p>\n<\/div>\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\/equation-de-la-tangente-ligne.webp\" alt=\"equazione tangente\" class=\"wp-image-2306\" width=\"463\" height=\"461\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Nell&#8217;immagine sopra puoi vedere una curva<\/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-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> rappresentato in blu e una linea arancione tangente alla funzione<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> Di<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd5304ac1643ba3660a7efa36ade1983_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"51\" style=\"vertical-align: -3px;\"><\/p>\n<p> , poich\u00e9 hanno solo questo punto in comune. Bene, l&#8217;equazione di questa tangente \u00e8<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-326424811181144df35c0b94ce50c462_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -y_0= m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<p> , e la sua pendenza \u00e8<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c606eb4b268b71562672c32a0461053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hallar-la-ecuacion-de-la-recta-tangente\"><\/span> Come trovare l&#8217;equazione della tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Per trovare l&#8217;equazione della tangente ad una funzione in un punto, devi fare:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">Trova la pendenza della linea tangente calcolando la derivata della funzione nel punto di tangenza.<\/span><\/li>\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">Determinare un punto sulla retta tangente.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>Trova l&#8217;equazione della linea tangente<\/strong> utilizzando la pendenza calcolata e il punto della linea tangente.<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-ecuacion-de-la-recta-tangente-a-una-curva\"><\/span> Esempio dell&#8217;equazione della tangente ad una curva<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Una volta vista la teoria sull&#8217;equazione della tangente, vediamo come calcolare l&#8217;equazione di una tangente risolvendo passo dopo passo un esempio:<\/p>\n<ul>\n<li> Calcolare l&#8217;equazione della tangente alla curva\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea8efcaacce7a90d3cc483105986c47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<p> Di<\/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> .<\/li>\n<\/ul>\n<p> Sappiamo che l&#8217;equazione della tangente \u00e8 sempre della forma seguente:<\/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-326424811181144df35c0b94ce50c462_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -y_0= m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> La prima cosa da fare \u00e8 calcolare la pendenza della retta. Pertanto, la pendenza della tangente,<\/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-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> , sar\u00e0 il valore della derivata della curva nel punto di tangenza x=1, cio\u00e8<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a69005ee8bf2d80d73b989ad0cedccd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<p> Pertanto differenziamo la funzione e poi calcoliamo <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eb68a498d3bd60e51d3dc230691f886c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" 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-92c9a5ee4068789701733f793fbac622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+x \\quad \\longrightarrow \\quad f'(x)=2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"293\" 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-d96270e9b7d7c3cae8baea602cea53bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(1)= 2\\cdot 1+1=2+1=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"218\" 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-2443a93bff265c6b8ba692ef8d14f633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(1)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Una volta che conosciamo il valore 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-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> , dobbiamo trovare un punto<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8e531a80c13865d1ad612bd3f634efa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x_0,y_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"54\" style=\"vertical-align: -5px;\"><\/p>\n<p> della retta tangente per completare l&#8217;equazione della retta tangente.<\/p>\n<p> L&#8217; <strong>equazione della tangente e della curva hanno sempre un punto in comune<\/strong> , che in questo caso \u00e8<\/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-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> . Quindi, come la curva<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> passa per questo punto, possiamo trovare l&#8217;altra componente del punto facendo il calcolo <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32045357853caad8774629c95963835d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" 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-ea8efcaacce7a90d3cc483105986c47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"108\" 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-7b2601f20b100f2635bc0342175b4627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(1)=1^2+1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Il punto di tangenza \u00e8 quindi:<\/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-d26257abb9047188ab3e3887f447e20a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sia la curva che la tangente passano per questo punto, quindi possiamo usarlo anche per trovare l&#8217;equazione della tangente.<\/p>\n<p> Non resta che sostituire i valori trovati della pendenza e del punto della tangente nella sua equazione:<\/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-0321e19825c08a1f47a00b2cf625088f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} y -y_0= m(x-x_0) \\\\[3ex] m=3 \\qquad P(1,2) \\end{array} \\right\\} \\longrightarrow \\ y -2= 3(x-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> In breve, l&#8217;equazione della tangente \u00e8: <\/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-037e5c42a4adef3e5ba970a66b8d3459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y-2=3(x-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<hr class=\"wp-block-separator has-text-color has-background is-style-wide\" style=\"background-color:#1976d2;color:#1976d2\">\n<p> Puoi anche esprimere l&#8217;equazione della retta tangente con l&#8217;equazione esplicita della retta: <\/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-59097f2ef899c7c608e2527467021b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=3x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<hr class=\"wp-block-separator has-text-color has-background is-style-wide\" style=\"background-color:#1976d2;color:#1976d2\">\n<p> Sotto potete vedere la curva rappresentata<\/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-ea8efcaacce7a90d3cc483105986c47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<p> e la sua retta tangente a <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2883f0b53c531552fde7ff189f83165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=1,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1020651b62576571e0ac9c0cb65dd287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-2=3(x-1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" 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\/equation-de-la-tangente-a-une-courbe-en-un-point.webp\" alt=\"equazione della retta tangente ad una curva in un punto\" class=\"wp-image-2318\" width=\"445\" height=\"434\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Come puoi vedere, la curva<\/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-ea8efcaacce7a90d3cc483105986c47c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2+x\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<p> e la tangente<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3cb3f64ce416f3a5c6cc80c11cae9afb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-2=3(x-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\"><\/p>\n<p> hanno in comune solo il punto<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42a32282c97c3b8d9f90b2f1418844d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<p> , esattamente come avevamo calcolato. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-de-la-recta-tangente\"><\/span> Esercizi risolti sull&#8217;equazione della tangente<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Esercizio 1<\/h3>\n<p> Calcolare l&#8217;equazione della tangente alla curva<\/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-99f623c4fede3b664682c5cbc1aab81d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2-4x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" style=\"vertical-align: -5px;\"><\/p>\n<p> Di <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-71e6033606cd14039ab202fb7a18c50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2 .\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> L&#8217;equazione della tangente sar\u00e0 sempre della forma seguente:<\/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-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>Passaggio 1: calcolare la pendenza della linea tangente<\/strong><\/p>\n<p class=\"has-text-align-left\"> La pendenza, <em>m<\/em> , \u00e8 il valore della derivata della curva nel punto di tangenza. Pertanto, in questo caso <\/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-c7192bf7bd4300d7d77fe084134d6849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = f'(2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" 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-ab9e97205d5c9f2fbfcb085cbfdbdd75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2-4x+3 \\ \\longrightarrow \\ f'(x)= 4x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"319\" 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-e3cb482f7e68631c8dcc5705ac1257d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(2)= 4\\cdot 2-4=8-4=4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"218\" 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-b0e7f5cd5a44a120769c9d3a1eae02c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(2)=4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>Passaggio 2: trova un punto sulla linea tangente<\/strong><\/p>\n<p class=\"has-text-align-left\"> L&#8217;equazione della tangente e della curva hanno sempre un punto in comune, che in questo caso \u00e8<\/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-c657687cbbf5ea9a7545edb42190e592_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> . Quindi, come la curva<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7ee323bc5a3f73ad5e066b13bed5504_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -5px;\"><\/p>\n<p> passa per questo punto, possiamo trovare l&#8217;altra componente del punto facendo il calcolo <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f026e401162db03299777455b748b308_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" 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-99f623c4fede3b664682c5cbc1aab81d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2-4x+3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"156\" 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-67ff5b86b2842fefbdf2ddc7c2df39f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(2)=2\\cdot 2^2-4\\cdot 2+3 =2 \\cdot 4 -8 +3 = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"326\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pertanto, il punto attraverso il quale passano sia la curva che la tangente \u00e8 il punto<\/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-d744fa34f41ed1bbe3fdf2c5ad7f55a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,3).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong>Passaggio 3: scrivere l&#8217;equazione della tangente<\/strong><\/p>\n<p class=\"has-text-align-left\"> Non resta che sostituire i valori trovati della pendenza e del punto della tangente nella sua equazione:<\/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-1622c6ecd4d43bb4fc4901b437464652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} y -y_0= m(x-x_0) \\\\[3ex] m=4 \\qquad P(2,3) \\end{array} \\right\\} \\longrightarrow \\ y -3= 4(x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> L&#8217;equazione della tangente \u00e8 quindi: <\/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-c1233301c390a75095fc24bd8765e081_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y -3= 4(x-2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" 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\">Esercizio 2<\/h3>\n<p> Calcolare l&#8217;equazione della tangente alla curva<\/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-d1309dcf6b647174b562cb71ab600c1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=-3x^2+2x\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"139\" style=\"vertical-align: -5px;\"><\/p>\n<p> all&#8217;origine delle coordinate. <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> L&#8217;origine delle coordinate si riferisce al punto<\/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-d5f3123d35179a39bd727675fca259c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dobbiamo quindi calcolare la tangente alla funzione in quel punto<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-791f3561f68c75b943d5af446c9f988f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0) .\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Per prima cosa determiniamo il valore della pendenza della tangente calcolando la derivata all&#8217;origine delle coordinate: <\/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-e3f5e3bd3a06eb5e2831d90e5fc0f31d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=-3x^2+2x \\ \\longrightarrow \\  f'(x)= -6x+2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"315\" 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-d07228d62a796c695cb75841830d0e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f'(0)= -6\\cdot 0+2=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" 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-075eebc763002b84e54211e61242356f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(0)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> In questo caso conosciamo gi\u00e0 il punto attraverso il quale passa la tangente. Perch\u00e9 l&#8217;affermazione ci dice che la retta deve essere tangente alla curva nell&#8217;origine delle coordinate, cio\u00e8 nel punto<\/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-d5f3123d35179a39bd727675fca259c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Quindi il punto in cui la curva e la tangente condividono \u00e8 il punto<\/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-d5f3123d35179a39bd727675fca259c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,0).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Infine, sostituisci semplicemente i valori trovati per la pendenza e il punto della tangente nella tua equazione:<\/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-de8e4e9dbb7a5bca1d591612abcf7730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} y -y_0= m(x-x_0) \\\\[3ex] m=2 \\qquad P(0,0) \\end{array} \\right\\} \\longrightarrow \\ y -0= 2(x-0)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> In conclusione, l\u2019equazione della tangente \u00e8: <\/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-19b9a613ed0c41d6c98ab37c6a0a1331_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -0= 2(x-0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" 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-329a7fc0d44a0b32cbb521e81ee50db6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y = 2x}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Esercizio 3<\/h3>\n<p> Calcola la linea tangente alla curva<\/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-33130a168a4e20b536fb742b8ce2a662_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=x^2-2x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\"><\/p>\n<p> che \u00e8 parallelo a destra<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b4e35094bc85458a54e2b47228f9c39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4x-6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"113\" style=\"vertical-align: -4px;\"><\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> In questo problema ci viene detto che la tangente deve essere parallela alla retta<\/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-02c5cab1d3747c5baa1ded66f3055f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4x-6=0 .\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<p> E due rette sono parallele se hanno la stessa pendenza. La tangente deve quindi avere la stessa pendenza della retta<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3dee6df2aaaef2e062c41a79057de62e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4x-6=0.\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ci\u00f2 significa che dobbiamo trovare la pendenza della retta<\/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-02c5cab1d3747c5baa1ded66f3055f61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4x-6=0 .\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"117\" style=\"vertical-align: -4px;\"><\/p>\n<p> Per fare ci\u00f2, cancelliamo la variabile e:<\/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-6390ce01aebdda3a7305c4dd1e55d4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-4x-6=0 \\ \\longrightarrow \\ y =4x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"246\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Quindi la pendenza della retta<\/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-824b16de72dde879834460d93bd88610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=4x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e8 4, poich\u00e9 la pendenza di una linea \u00e8 il numero che moltiplica la x quando la y \u00e8 chiara.<\/p>\n<p class=\"has-text-align-left\"> Quindi anche la pendenza della tangente deve essere 4, perch\u00e9 per essere parallele devono avere la stessa pendenza.<\/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-e5072b7479ca854c5e3cdea8ffff2c0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> In questo caso non ci dicono il punto di tangenza tra la curva e la tangente. Ma sappiamo che la derivata della curva nel punto di tangenza \u00e8 uguale alla pendenza della tangente, cio\u00e8<\/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-5c606eb4b268b71562672c32a0461053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Ebbene, come possiamo conoscere il valore di<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> , possiamo trovare x <sub>0<\/sub> dall&#8217;equazione<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f79089d702fc8e5b6b7342c0eb2f0c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Per fare ci\u00f2, calcoliamo prima la derivata 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-40e51e628d64bea41578e16139b71b6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" 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-ac4abafb3c879a6fd9c906ff9eea94d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= x^2-2x-1 \\ \\longrightarrow \\ f'(x)=2x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"309\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E ora risolviamo<\/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-5c606eb4b268b71562672c32a0461053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> sapendo che <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-421352ccc778c624805a5e2663bb7077_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = 4 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" 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-f99f5b23457229b93eb24c214942f41f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m =f'(x_0)\" 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-6a9fc1e268bfa17b6fe04e5fafbaaedc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 =2(x_0)-2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-74d7e6af89f911f5a194fee138e70afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4+2 =2x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: -3px;\"><\/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-96c892854007fa06281252d3fcc3ae4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6 =2x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: -3px;\"><\/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-9602ea885075b53499286a5126ad9724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{2} =x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"49\" 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-f2fb028e2d1cb1011436226f865d5162_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3=x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E una volta che conosciamo la coordinata x del punto, possiamo trovare l&#8217;altra coordinata del punto eseguendo i calcoli <\/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-4763abfc9310baf690c4bb81c5d8b743_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"42\" 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-9e36063894754424dc75ff41070c42ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(3)=3^2-2\\cdot 3-1= 9-6-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"281\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pertanto, il punto attraverso il quale passano sia la curva che la tangente \u00e8 il punto<\/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-a3558010337a7cdc27dddb44c10f0df1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Non resta che sostituire i valori trovati della pendenza e del punto della tangente nella sua equazione:<\/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-8f1f49e9bef505c5c71cffd15f0d29d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} y -y_0= m(x-x_0) \\\\[3ex] m=4 \\qquad P(3,2) \\end{array} \\right\\} \\longrightarrow \\ y -2= 4(x-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"344\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E l&#8217;equazione della tangente \u00e8: <\/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-89b6fd61abd22d30db13453334da7135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y -2=4(x-3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" 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\">Esercizio 4<\/h3>\n<p> Calcola la linea tangente alla curva<\/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-ab7fb2898ec2a42b558f032b99518338_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2+5x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<p> che forma un angolo di 45\u00ba con l&#8217;asse X. <\/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>Vedi la soluzione<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> La formulazione del problema ci dice che la linea tangente deve formare un angolo di 45\u00ba con l&#8217;asse X. In questi casi \u00e8 necessario applicare la seguente formula per trovare il valore della pendenza: <\/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-1e17ba52bc8d7a78aa6abe918856ba28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}\\left(\\alpha\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" 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-c891eec41f7529fbb36d622027b94d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = \\text{tg}\\left(45^{\\text{o}}\\right) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"129\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> La dichiarazione non specifica il punto di tangenza tra la curva e la linea tangente. Ma sappiamo che la derivata della curva nel punto di tangenza \u00e8 equivalente alla pendenza della tangente, cio\u00e8<\/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-5c606eb4b268b71562672c32a0461053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Possiamo quindi calcolare x <sub>0<\/sub> risolvendo l&#8217;equazione<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f79089d702fc8e5b6b7342c0eb2f0c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Per fare ci\u00f2, calcoliamo prima la derivata 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-40e51e628d64bea41578e16139b71b6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" 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-d757979ec817338abf9a0d50e4d8838d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=2x^2+5x+1\\ \\longrightarrow \\ f'(x)=4x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"318\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E ora risolviamo<\/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-5c606eb4b268b71562672c32a0461053_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m=f'(x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<p> sapendo che <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32704d9853b0093395b41eb385ebb4e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = 1 :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" 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-f99f5b23457229b93eb24c214942f41f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m =f'(x_0)\" 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-eec283acc7af9f75a48ed262d785d7f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1 =4(x_0)+5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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-4bcad96ea71d673fba2f814bffaee7c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-5 =4x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"88\" style=\"vertical-align: -3px;\"><\/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-7638e49e3e5eab4f64f4dc439d458ec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-4 =4x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -3px;\"><\/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-8561c7a3def54db216a8f1ebf2588e79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-4}{4} =x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" 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-64d0311d2aa3328e9ed1f2073e90e4bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1=x_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"62\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E una volta che conosciamo la coordinata x del punto, possiamo trovare l&#8217;altra coordinata del punto eseguendo i calcoli <\/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-ab353a75f8c672950ea7d8376104722d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" 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-33f491d7f9d0eeeb767d846b5650734f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-1)=2(-1)^2+5(-1)+1=2\\cdot 1  -5 + 1 = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"382\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">Pertanto, il punto attraverso il quale passano sia la curva che la tangente \u00e8 il punto<\/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-d2ae436ead5cc58de912263561cfbe63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-1,-2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Non resta che sostituire i valori trovati della pendenza e del punto della tangente nella sua equazione:<\/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-8ed772b3993de50c4c67631a6fd33040_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} y -y_0= m(x-x_0) \\\\[3ex] m=1 \\qquad P(-1,-2) \\end{array} \\right\\} \\longrightarrow \\ y -(-2)= 1(x-(-1))\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"414\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> E infine, eseguiamo le operazioni per trovare l&#8217;equazione della tangente: <\/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-28409d87564a3385166261f1fe92c01e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y -(-2)=1(x-(-1))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" 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-9ebfc08d88b0dcf9c22ff7f225afdabf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y +2=1(x+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" 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-b1c1b9eabdc99bc1ff5b5e8cdb5baf94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y + 2=x+1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"103\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In questo articolo vedremo come trovare l&#8217;equazione della tangente ad una curva. Inoltre, puoi allenarti con esercizi risolti di diversi livelli di difficolt\u00e0. Equazione della retta tangente ad una funzione in un punto L&#8217; equazione della tangente alla funzione f(x) nel punto x=x 0 \u00e8: Dove il punto P(x 0 ,y 0 ) \u00e8 il &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/it\/equazione-tangente\/\"> <span class=\"screen-reader-text\">Equazione della retta tangente<\/span> Leggi altro &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":[17],"tags":[],"class_list":["post-42","post","type-post","status-publish","format-standard","hentry","category-rappresentazione-delle-funzioni"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equazione della linea tangente -<\/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\/it\/equazione-tangente\/\" \/>\n<meta property=\"og:locale\" content=\"it_IT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equazione della linea tangente -\" \/>\n<meta property=\"og:description\" content=\"In questo articolo vedremo come trovare l&#8217;equazione della tangente ad una curva. Inoltre, puoi allenarti con esercizi risolti di diversi livelli di difficolt\u00e0. Equazione della retta tangente ad una funzione in un punto L&#8217; equazione della tangente alla funzione f(x) nel punto x=x 0 \u00e8: Dove il punto P(x 0 ,y 0 ) \u00e8 il &hellip; Equazione della retta tangente Leggi altro &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/it\/equazione-tangente\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T10:58:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-326424811181144df35c0b94ce50c462_l3.png\" \/>\n<meta name=\"author\" content=\"Squadra di Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Scritto da\" \/>\n\t<meta name=\"twitter:data1\" content=\"Squadra di Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo di lettura stimato\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minuti\" \/>\n<script type=\"application\/ld+json\" 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