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 )

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

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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a is done please show b

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Chapter 4 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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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].