Explanation Given: The function is: f ( x ) = 2 x 3 − 5 x 2 − 4 x + 2 Formula used: The derivative property as; d d x ( x n ) = n x n − 1 Calculation: Consider the provided function, f ( x ) = 2 x 3 − 5 x 2 − 4 x + 2 In order to find the intervals, calculate f ' ( x ) . Then, f ' ( x ) = d d x ( 2 x 3 − 5 x 2 − 4 x + 2 ) = 6 x 2 − 10 x − 4 Now, equate f ' ( x ) to 0. 6 x 2 − 10 x − 4 = 0 6 x 2 − 12 x + 2 x − 4 = 0 6 x ( x − 2 ) + 2 ( x − 2 ) = 0 ( x − 2 ) ( 6 x + 2 ) = 0 Further simplification, x = 2 , − 1 3 The function f ( x ) is increasing when f ' ( x ) > 0 and decreasing when f ' ( x ) < 0

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Author: MULLINS

Publisher: YUZU

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Chapter 12.1, Problem 13E

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To calculate: The interval on which the function f(x)=2x3−5x2−4x+2 is increasing or decreasing.

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Chapter 12.1, Problem 10E

Chapter 12.1, Problem 12E

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The interval on which the function f ( x ) = 2 x 3 − 5 x 2 − 4 x + 2 is increasing or decreasing.

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To calculate: The interval on which the function f(x)=2x3−5x2−4x+2 is increasing or decreasing.

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Chapter 12 Solutions