Explanation Given: The function is y = | x 2 + 4 x − 12 | and the interval is [ 0 , 4 ] . The graph of the function y = | x 2 + 4 x − 12 | 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 = | x 2 + 4 x − 12 | …..(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 2 the value of the function starts increasing. At the point x = 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 = 2 . Since, if the function is not continuous at x = 2 then the function is not differentiable at x = 2 . This implies that y ′ ( x ) does not exists for x = 2 . Therefore, the critical point for the given function is x = 2 . To obtain the maximum and minimum value of the given function on the interval [ 0 , 4 ] , check the value of y ( 0 ) , y ( 2 ) and y ( 4 )

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.2, Problem 67E

To determine

To find:

The critical points and the extreme values of the function y=|x2+4x−12| on the interval [0,4].

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Chapter 4.2, Problem 66E

Chapter 4.2, Problem 68E

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Chapter 4 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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The critical points and the extreme values of the function y = | x 2 + 4 x − 12 | on the interval [ 0 , 4 ] .

Solution Summary: The graph of the function y=left|x2+4x-12right| is redrawn as shown in Figure 1

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To find:

The critical points and the extreme values of the function y=|x2+4x−12| on the interval [0,4].

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Chapter 4 Solutions

The critical points and the extreme values of the function y = | x 2 + 4 x − 12 | on the interval [ 0 , 4 ] .

Solution Summary: The graph of the function y=left|x2+4x-12right| is redrawn as shown in Figure 1

Concept explainers

Videos

To find: The critical points and the extreme values of the function y=|x2+4x−12| 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=|x2+4x−12| on the interval [0,4].