Explanation Given information: The provided function is: h ( x ) = 1 − x 2 , for − 4 ≤ x < 0 h ( x ) = 1 − x , for 0 < x ≤ 1 h ( x ) = x − 1 , for 1 ≤ x ≤ 2 . Formula used: Do the following steps to find the absolute extrema of the function over an interval: Step 1. Find the value of f ′ ( x ) . Step 2. Find the critical values. Step 3. If the interval is closed and there is more than one critical value then use maximum-minimum Principle 1. Step 4. If the interval is closed and there is exactly one critical value use either maximum-minimum Principle 1 or maximum-minimum Principle 2. Step 5. If the interval is not closed and the function has only one critical point then use Maximum-minimum Principle 2. In this case the function has either only maximum or only minimum. Calculation: Consider the provided function: h ( x ) = 1 − x 2 , for − 4 ≤ x < 0 h ( x ) = 1 − x , for 0 < x ≤ 1 h ( x ) = x − 1 , for 1 ≤ x ≤ 2 . Now, look at each piece of function for any critical values as: For − 4 < x < 0 : h ' ( x ) = − 2 x For 0 < x < 1 : h ' ( x ) = − 1 For 1 ≤ x ≤ 2 : h ' ( x ) = 1 Therefore, there are no critical values of h ( x ) in the provided intervals

Calculus and Its Applications (11th Edition)

11th Edition

ISBN: 9780321979391

Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent

Publisher: PEARSON

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Chapter 2.4, Problem 109E

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To calculate: The absolute maximum and minimum values of function h(x)=1−x2 for −4≤x<0 and h(x)=1−x for 0<x≤1 and h(x)=x−1 for 1≤x≤2 and also sketch graph.

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Chapter 2.4, Problem 108E

Chapter 2.4, Problem 110E

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Calculus and Its Applications (11th Edition)

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The absolute maximum and minimum values of function h ( x ) = 1 − x 2 for − 4 ≤ x < 0 and h ( x ) = 1 − x for 0 < x ≤ 1 and h ( x ) = x − 1 for 1 ≤ x ≤ 2 and also sketch graph.

Solution Summary: The author explains the formula used to find the absolute extrema of the function over an interval.

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To calculate: The absolute maximum and minimum values of function h(x)=1−x2 for −4≤x<0 and h(x)=1−x for 0<x≤1 and h(x)=x−1 for 1≤x≤2 and also sketch graph.

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The absolute maximum and minimum values of function h ( x ) = 1 − x 2 for − 4 ≤ x &lt; 0 and h ( x ) = 1 − x for 0 &lt; x ≤ 1 and h ( x ) = x − 1 for 1 ≤ x ≤ 2 and also sketch graph.

Solution Summary: The author explains the formula used to find the absolute extrema of the function over an interval.

Concept explainers

Videos

To calculate: The absolute maximum and minimum values of function h(x)=1−x2 for −4≤x<0 and h(x)=1−x for 0<x≤1 and h(x)=x−1 for 1≤x≤2 and also sketch graph.

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Chapter 2 Solutions

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The absolute maximum and minimum values of function h ( x ) = 1 − x 2 for − 4 ≤ x < 0 and h ( x ) = 1 − x for 0 < x ≤ 1 and h ( x ) = x − 1 for 1 ≤ x ≤ 2 and also sketch graph.