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# Solution: Find equations of the tangent line and normal line

ISBN: 9780538497817 125

## Solution for problem 50 Chapter 2

Calculus, | 7th Edition

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Calculus, | 7th Edition

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Problem 50

Find equations of the tangent line and normal line to the curve at the given point. 2 4xy y2 13 y

Step-by-Step Solution:
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4.2 What Derivatives T ells Us I. What first derivatives tells us Increasing/Decreasing Test (I/D Test)  If f ‘ > 0 on interval  f is increasing on the interval  If f ‘ < 0 on interval  f is decreasing on the interval  F is decreasing on (-5,-2) (0,5)  F ‘ < 0  F is increasing on (-2,0)  F ‘ > 0  Corner points f ‘ DNE o F ‘ (-2) DNE, F ‘ (0) DNE  F is increasing on (-4,-3) (-1,1)  f ‘ < 0  F is decreasing on (-3,-1) (2,2)  f ‘ > 0  F ‘ (-3) = f ‘ (-1) = f ‘ (1) = 0 EXAMPLE 1: Sketching a function f(x) continuous on its domain (- ,) satisfying the following conditions. (1) F ‘ > 0 on (- , 0), (4,6) and (6, )  [ f increasing on (- , 0), (4,6) and (6, ) ] (2) f ‘

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Solution: Find equations of the tangent line and normal line