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Math

Calculus

Find an equation of the tangent line to the curve at the giv

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 43E

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Question

47-48 Find an equation of the tangent line to the curve at the given point.

Expert Solution

Step 1

$\sin c e w e k n o w t h a t i f y = f (x) b e a n u c u r v e t h e n i t s \tan g e n t l i n e s l o p e a t p o i n t (x_{1}, y_{2}) i s m = f' (x_{1}) t h e n i t s \tan g e n t l i n e e q u a t i o n i s : - y - y_{1} = m (x - x_{1})$

(48)

$g i v e n c u r v e i s y = \sqrt{1 + x^{3}} t h e n w e h a v e t o f i n d i t s \tan g e n t l i n e e q u a t i o n a t p o i n t (2, 3)$

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