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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

23-42 Find f.

f ( x ) = x 2 / 3 + x 2 / 3

To determine

To find:

The function f(x)

Explanation

1) Concept:

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is, Fx+c where c is an arbitrary constant.

2) Definition:

A function F  is called an antiderivative of f on an interval I if F'x=fx f for all x in I.

3) Given:

f''x=x2/3+x-2/3 

4) Calculations:

f''x=x2/3+x-2/3

The general antiderivative of f''x using power rule of antiderivative

 f'x=x5353-x1313+C

 f'x=35x53-31x13+C

f'x=35x53-3x13+C

Using power rules of antiderivative once more,

 fx=3

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