Explanation Definition used: Increasing function: Let f be a function defined on some interval with derivatives at each point. Then the function is said to be increasing if f ′ ( x ) > 0 holds for each x in the interval. Decreasing function: Let f be a function defined on some interval with derivatives at each point. Then the function is said to be decreasing if f ′ ( x ) < 0 holds for each x in the interval. Critical point: A point whose x- coordinate is the critical number c such that either f ′ ( c ) = 0 or f ′ ( c ) does not exists and y -coordinate is f ( c ) . Calculation: The given function is f ( x ) = − x 3 − 2 x 2 + 15 x + 10 . Compute the derivative of the function f ( x ) = − x 3 − 2 x 2 + 15 x + 10 and obtain the intervals. f ′ ( x ) = − 3 x 2 − 4 x + 15 . Set f ′ ( c ) = 0 and find the critical number. f ′ ( c ) = − 3 c 2 − 4 c + 15 0 = − 3 c 2 − 4 c + 15 0 = − 3 c 2 − 4 c + 15 Factorise the above quadratic equation as follows. 3 c 2 + 4 c − 15 = 0 3 c 2 + 9 c − 5 c − 15 = 0 3 c ( c + 3 ) − 5 ( c + 3 ) = 0 − ( 3 c − 5 ) ( c + 3 ) = 0 The critical numbers are c = 5 3 or c = − 3 . The function has tangent at the points 5 3 or − 3 as the derivative at these points is 0. These points determines the intervals, ( − ∞ , − 3 ) , ( − 3 , 5 3 ) , ( 5 3 , ∞ ) . Consider a point from each interval and find the corresponding value of the derivative function

10th Edition

ISBN: 8220102020252

Author: RITCHEY

Publisher: PEARSON

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Chapter 13.1, Problem 2YT

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To find: The intervals in which the function is increasing or decreasing and graph the function.

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Chapter 13 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

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 intervals in which the function is increasing or decreasing and graph the function.

Solution Summary: The author explains how to find the intervals in which the function is increasing or decreasing and graph it.

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To find: The intervals in which the function is increasing or decreasing and graph the function.

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Chapter 13 Solutions