   Chapter 4.9, Problem 35E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find f.f′(x) = 5x2/3, f(8) = 21

To determine

To find: The general antiderivative for the function f(x)=5x23,f(8)=21 .

Explanation

Given Data:

Write the given function as follows.

f(x)=5x23,f(8)=21

Formula used:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

Calculation of f(x) :

Write the function as follows.

f(x)=5x23 (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows.

f(x)=5(x23+123+1)+C=5(x5353)+C

f(x)=3x53+C (2)

As f(8)=21 , substitute 8 for x in equation (2),

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