{"id":143503,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/how-do-i-find-the-equation-for-a-tangent-line-without-derivatives"},"modified":"2017-08-17T11:42:40","modified_gmt":"2017-08-17T11:42:40","slug":"how-do-i-find-the-equation-for-a-tangent-line-without-derivatives","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/how-do-i-find-the-equation-for-a-tangent-line-without-derivatives\/","title":{"rendered":"How do I find the equation for a tangent line without derivatives?"},"content":{"rendered":"<p>The equation of the tangent line is the remainder when you divide by (x-a)^2.<\/p>\n<p>It&#8217;s EASY for polynomials. You have to examine the analytic geometry of polynomial division and you will find that 1. division by (x-a)(x-b) gives a remainder that is the secant line intersecting the graph at x=a and x=b, 2. division by (x-a)^2 yields a remainder which is the tangent line at x=a. It&#8217;s EASY for rational and algebraic functions too. To handle rational or algebraic functions, write the function as a polynomial in two variables, x and y, as in F(x,y) = 0, and expand to first order. That fist order equation is the equation for the tangent line. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>The equation of the tangent line is the remainder when you divide by (x-a)^2. It&#8217;s EASY for polynomials. You have to examine the analytic geometry of polynomial division and you will find that 1. division by (x-a)(x-b) gives a remainder <a href=\"https:\/\/www.benedictsol.com\/blogs\/how-do-i-find-the-equation-for-a-tangent-line-without-derivatives\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-143503","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=143503"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/143503\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=143503"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=143503"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=143503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}