   Chapter 3.9, Problem 29E

Chapter
Section
Textbook Problem

# 23-42 Find f. f ′ ( x ) = 1 + 3 x ,    f ( 4 ) = 25

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=1+3x, f4=25

4) Calculations:

Here f'x=1+3x

f'x=1+3x12

The general antiderivative of f'x using rules of antiderivative is,

fx=x+3x3232+C

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