Explanation Given: The function is y = | cos x | and the interval is [ 0 , 4 ] . The graph of the function y = | cos x | is redrawn as shown in Figure 1 . Concept used: Critical points: For a function f ( x ) , critical points are the points at which the value of f ′ ( x ) is zero or f ′ ( x ) does not exists. Calculation: The given function is expressed as follows: y = | cos x | …..(1) Figure 1 represents the graph of the given function. From Figure 1 it is observed that in the interval [ 0 , 4 ] as the value of x is increased the value of the function decreases and as x reaches a value of π 2 the value of the function starts increasing. At the point x = π 2 the curve of the function has a sharp edge or it can be said that the function is not continuous at the point x = π 2 . Since, if the function is not continuous at x = π 2 then the function is not differentiable at x = π 2 . This implies that y ′ ( x ) does not exists for x = π 2 . From Figure 1 it is observed that at the point x = 0 and x = π the slope of the function is zero. Therefore, the critical point for the given function is x = 0 , x = π 2 and x = π . To obtain the maximum and minimum value of the given function on the interval [ 0 , 4 ] , check the value of y ( 0 ) , y ( π 2 ) , y ( π ) and y ( 4 )

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 4.2, Problem 68E

To determine

To find:

The critical points and the extreme values of the function y=|cosx| on the interval [0,4].

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Chapter 4.2, Problem 67E

Chapter 4.2, Problem 69E

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Chapter 4 Solutions

Calculus: Early Transcendentals

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The critical points and the extreme values of the function y = | cos x | on the interval [ 0 , 4 ] .

Solution Summary: The graph of the function y=left|mathrmcosxright| is redrawn as shown in Figure 1.

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The critical points and the extreme values of the function y=|cosx| on the interval [0,4].

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Chapter 4 Solutions

The critical points and the extreme values of the function y = | cos x | on the interval [ 0 , 4 ] .

Solution Summary: The graph of the function y=left|mathrmcosxright| is redrawn as shown in Figure 1.

Concept explainers

Videos

To find: The critical points and the extreme values of the function y=|cosx| on the interval [0,4].

Want to see the full answer?

Chapter 4 Solutions

To find:

The critical points and the extreme values of the function y=|cosx| on the interval [0,4].