Explanation Given information: A function y = sin ( x 4 ) . Formula used: Derivative of sin x , d d x sin x = cos x Chain rule of a differential, d d x f t = d d t f t ⋅ d t d x Differentia of exponent x n , d d x x n = n x n − 1 Product rule, ( f ⋅ g ) ′ = f ′ g + g ′ f Calculation: Consider the function y = sin ( x 4 ) . Calculate the first differential as below. Use the chain rule. d d x y = d d x sin ( x 4 ) y ′ = cos x 4 ⋅ d d x ( x 4 ) = cos x 4 ⋅ 4 x 3 = 4 x 3 cos x 4 At the input argument x = 10 . y ′ ( 10 ) = 4 ( 10 ) 3 cos ( 10 4 ) = 4000 cos ( 10 4 ) > 0 Thus, the function is increasing

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ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 3.5, Problem 24P

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If the function y=sin(x4) is increasing or decreasing at the point where x=10.

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Chapter 3.5, Problem 23P

Chapter 3.5, Problem 25P

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If the function y = sin ( x 4 ) is increasing or decreasing at the point where x = 10 .

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To calculate: If the function y=sin(x4) is increasing or decreasing at the point where x=10.

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Chapter 3 Solutions

To calculate:

If the function y=sin(x4) is increasing or decreasing at the point where x=10.