Explanation Approach: 1. Locate the critical numbers for f on a number line, as well as any points where f is undefined. These points determine several open intervals. 2. Choose a value of x in each of the intervals determine in step 1. Use these values to determine whether f ′ ( x ) > 0 or f ′ ( x ) < 0 in that interval. 3. Determine whether f is increasing or decreasing on the interval. Calculation: Consider the given function: f ( x ) = − x 3 + 2 x 2 + 15 x + 16 Differentiate the function with respect to x : f ′ ( x ) = − 3 x 2 + 4 x + 15 Find the critical numbers: − 3 x 2 + 4 x + 15 = 0 3 x 2 − 4 x − 15 = 0 ( x − 3 ) ( 3 x + 5 ) = 0 x = 3 , − 5 3 Choose the random point − 3 in the interval ( − ∞ , − 5 3 ) .

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 5.CR, Problem 19CR

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The interval in which the given function f(x)=−x3+2x2+15x+16 is increasing and decreasing.

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Chapter 5.CR, Problem 18CR

Chapter 5.CR, Problem 20CR

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Ch. 5.1 - YOUR TURN Find where the function is increasing...Ch. 5.1 - YOUR TURN 2 Find the intervals in which...Ch. 5.1 - Prob. 3YT Ch. 5.1 - YOUR TURN Find where f is increasing and...Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Find the open intervals where the functions...Ch. 5.1 - Prob. 6E

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The interval in which the given function f ( x ) = − x 3 + 2 x 2 + 15 x + 16 is increasing and decreasing.

Solution Summary: The author explains how to find the interval in which the given function f(x) is increasing and decreasing.

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To find:

The interval in which the given function f(x)=−x3+2x2+15x+16 is increasing and decreasing.

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Chapter 5 Solutions

The interval in which the given function f ( x ) = − x 3 + 2 x 2 + 15 x + 16 is increasing and decreasing.

Solution Summary: The author explains how to find the interval in which the given function f(x) is increasing and decreasing.

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To find: The interval in which the given function f(x)=−x3+2x2+15x+16 is increasing and decreasing.

Want to see the full answer?

Chapter 5 Solutions

To find:

The interval in which the given function f(x)=−x3+2x2+15x+16 is increasing and decreasing.