Explanation Given: Consider the given graph as shown below in figure 1. Definition used: Relative extremum: A function is said to have a relative extremum at c if it has either a relative maximum or relative minimum at c . Relative maximum: A function is said to have a relative maximum at c if there exists an open interval ( a , b ) that contains c such that f ( x ) ≤ f ( c ) where c is a number in the domain of a function f . Relative minimum: A function is said to have a relative minimum at c if there exists an open interval ( a , b ) that contains c such that f ( x ) ≥ f ( c ) where c is a number in the domain of a function f . Increasing function: Let f be a function defined on some interval. Then the function is said to be increasing if for two numbers x 1 and x 2 , the inequality f ( x 1 ) < f ( x 2 ) holds when x 1 < x 2 . Decreasing function: Let f be a function defined on some interval. Then the function is said to be decreasing if for two numbers x 1 and x 2 , the inequality f ( x 1 ) > f ( x 2 ) holds when x 1 < x 2 . Calculation: Consider the given function in the graph as f ( x ) . From the preceding section it is obtained that the function decreases in the interval ( − ∞ , − 3 ) , increases in the interval ( − 3 , 0 ) , decreases in the interval ( 0 , 3 ) and again increases in the interval ( 3 , ∞ ) . That means the function change decreasing to increasing at − 3 from increasing to decreasing at 0 and then changes from decreasing to increasing at 3. Note that at x = − 3 , the value of function is f ( − 3 ) = 0 , at x = 0 , the value of function is f ( 0 ) = 4 and at x = 3 , the value of function is f ( 3 ) = 0

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 13.2, Problem 8E

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To find: The location and value of relative extrema that are present on the given graph

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Chapter 13.2, Problem 7E

Chapter 13.2, Problem 9E

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Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

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The location and value of relative extrema that are present on the given graph

Solution Summary: The author explains that relative extrema occur at x=0, and the relative minima occurs at 3 and 3 respectively.

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To find: The location and value of relative extrema that are present on the given graph

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Chapter 13 Solutions