(a) Explanation Given Information: The function is f ( x ) = 2 x + x 4 3 and point is x = 8 . Formula used: Sum rule of derivative is [ f + g ] ' ( x ) = f ' ( x ) + g ' ( x ) . Power rule for finding the derivative of function f ( x ) = x n is f ' ( x ) = n x n − 1 where n is any constant. Constant multiple rule of derivative is f ' ( c x ) = c f ' ( x ) , where c is any constant. Calculation: Consider the function, f ( x ) = 2 x + x 4 3 Apply sum rule of derivative with respect to x , f ' ( x ) = d d x ( 2 x + x 4 3 ) = d d x ( 2 x ) + d d x ( x 4 3 ) Apply constant multiple rule, f ' ( x ) = 2 d d x ( x ) + d d x ( x 4 3 ) Apply power rule, f (b) To determine To calculate: The derivative of function f ( x ) = 2 x + x 4 3 at x = 0 if it exists.

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Question

Chapter 11.1, Problem 74E

(a)

To determine

To calculate: The derivative of function f(x)=2x+x43 at x=8 if it exists.

(b)

To determine

To calculate: The derivative of function f(x)=2x+x43 at x=0 if it exists.

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Chapter 11.1, Problem 73E

Chapter 11.1, Problem 75E

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The derivative of function f ( x ) = 2 x + x 4 3 at x = 8 if it exists.

Solution Summary: The author explains how to calculate the derivative of function f(x)=2x+x 43 if it exists.