Explanation Given: The given function is f ( x ) = 1 4 x 8 − 1 2 x 6 − x 2 + 2 . Formula used: d d x ( x n ) = n x n − 1 Calculation: Differentiate the given function with respect to x . f ' ( x ) = d d x ( 1 4 x 8 − 1 2 x 6 − x 2 + 2 ) = 1 4 ⋅ 8 x 8 − 1 − 1 2 ⋅ 6 x 6 − 1 − 2 x 2 − 1 + 0 = 2 x 7 − 3 x 5 − 2 x Now, differentiate f ' ( x ) with respect to $x$. f ″ ( x ) = d d x ( 2 x 7 − 3 x 5 − 2 x ) = 2 ⋅ 7 x 7 − 1 − 3 ⋅ 5 x 5 − 1 − 2 ⋅ 1 = 14 x 6 − 15 x 4 − 2 Now, differentiate the function f ″ ( x ) with respect to x

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.2, Problem 22PS

To determine

To find f′,f″,f‴,f(4) for the function f(x)=14x8−12x6−x2+2 .

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Chapter 3.2, Problem 21PS

Chapter 3.2, Problem 23PS

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Chapter 3 Solutions

Calculus

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To find f ′ , f ″ , f ‴ , f ( 4 ) for the function f ( x ) = 1 4 x 8 − 1 2 x 6 − x 2 + 2 .

Solution Summary: The author explains how to differentiate the given function with respect to x.

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To find f′,f″,f‴,f(4) for the function f(x)=14x8−12x6−x2+2 .

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Chapter 3 Solutions