solution<\/h4>\nd<\/strong>.<\/p>\n
remember, the purpose of this question is to estimate<\/em> the zero. first of all, the tangent line approximation is nothing more than a linearization. we’ll need to know the derivative:<\/p>\n
<\/p>\n
then find the expression for l<\/em>(x<\/em>). note that g<\/em>(-1) ≈ 2.13 and g<\/em> '(-1) = 3.<\/p>\n
l<\/em>(x<\/em>) = 2.13 + 3(x<\/em> – (-1)) = 5.13 + 3x<\/em>.<\/p>\n
finally to find the zero, set l<\/em>(x<\/em>) = 0 and solve for x<\/em><\/p>\n
0 = 5.13 + 3x<\/em> → x<\/em> = -5.13\/3 = -1.71<\/p>\n","protected":false},"excerpt":{"rendered":"
what is linear approximation? basically, it’s a method from calculus used to “straighten out” the graph of a function near a particular point. scientists often use linear approximation to understand complicated relationships among variables. in this review article, we’ll explore the methods and applications of linear approximation. we’ll also take a look at plenty of […]<\/p>\n","protected":false},"author":223,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[240],"tags":[241],"ppma_author":[24932],"class_list":["post-12430","post","type-post","status-publish","format-standard","hentry","category-ap","tag-ap-calculus"],"acf":[],"yoast_head":"\nlinear approximation: ap calculus exam review - magoosh blog | high school<\/title>\n<meta name=\"description\" content=\"in this review article, we'll take a look at plenty of examples of linear approximation to better prepare you for the ap 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