Explanation Given: The given function is f ( x ) = x 5 − 5 x 3 + x + 12 . 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 ( x 5 − 5 x 3 + x + 12 ) = 5 x 5 − 1 − 5 ⋅ 3 x 3 − 1 + 1 + 0 = 5 x 4 − 15 x 2 + 1 Now, differentiate f ' ( x ) with respect to $x$. f ″ ( x ) = d d x ( 5 x 4 − 15 x 2 + 1 ) = 5 ⋅ 4 x 4 − 1 − 15 x 2 − 1 + 0 = 20 x 3 − 15 x Now, differentiate the function f ″ ( x ) with respect to x

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 3.2, Problem 21PS

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To find f′,f″,f‴,f(4) for the function f(x)=x5−5x3+x+12 .

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Chapter 3.2, Problem 20PS

Chapter 3.2, Problem 22PS

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Chapter 3 Solutions

Calculus

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To find f ′ , f ″ , f ‴ , f ( 4 ) for the function f ( x ) = x 5 − 5 x 3 + x + 12 .

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)=x5−5x3+x+12 .

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Chapter 3 Solutions