Explanation Given: f ( x ) = x 4 − 2 x 3 − 5 Calculation: Consider the function. f ( x ) = x 4 − 2 x 3 − 5 Differentiating with respect to x, we get f ′ ( x ) = 4 x 3 − 6 x 2 Again differentiating with respect to x, we get f ″ ( x ) = 12 x 2 − 12 x Now to find point of inflection, we solve the second derivative by setting it to zero, that is f ″ ( x ) = 0 ⇒ 12 x 2 − 12 x = 0 ⇒ 12 x ( x − 1 ) = 0 ⇒ x = 0 or x = 1 Now the sign chart of second derivative is,

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.3, Problem 43S

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To find the intervals on which the function f(x)=x4−2x3−5 is concave up or concave down.

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Chapter 3.3, Problem 42S

Chapter 3.3, Problem 44S

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To find the intervals on which the function f ( x ) = x 4 − 2 x 3 − 5 is concave up or concave down.

Solution Summary: The author explains how the function f(x) is concave up in the intervals and the second derivative by setting it to zero.

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To find the intervals on which the function f(x)=x4−2x3−5 is concave up or concave down.

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Chapter 3 Solutions