Explanation Given: The function is y = | x − 2 | and the interval is [ 0 , 4 ] . 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 shown below: y = | x − 2 | …..(1) Critical points are the points at which the value of f ′ ( x ) is zero or f ′ ( x ) does not exists. The given function is a modulus function and a modulus function is expressed as follows: y = { x x ≥ 0 − x x < 0 Similarly, the given function is expressed as follows: y = { x − 2 x ≥ 2 − ( x − 2 ) x < 2 For x ≥ 2 the derivative of the given function is calculated as shown below: y ′ = d ( x − 2 ) d x = 1 This implies that in the interval [ 2 , ∞ ) the first derivative of the function is y ′ = 1 . For x ≤ 2 the derivative of the given function is calculated as shown below: y ′ = d ( − ( x − 2 ) ) d x = d ( − x + 2 ) d x = − 1 This implies that in the interval ( − ∞ , 2 ] the first derivative of the function is y ′ = − 1

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.2, Problem 65E

To determine

To find:

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

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Chapter 4.2, Problem 64E

Chapter 4.2, Problem 66E

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Chapter 4 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

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

Solution Summary: The author explains the critical points and extreme values of the function y=left|x-2right| on the interval

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

Solution Summary: The author explains the critical points and extreme values of the function y=left|x-2right| on the interval

Concept explainers

Videos

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