   Chapter 3.9, Problem 47E

Chapter
Section
Textbook Problem

# The graph of a function is shown in the figure. Make a rough sketch of an antiderivative F, given that F ( 0 ) = 1 . To determine

To make:

A rough sketch of an antiderivative F(x).

Explanation

Explanations:

1) Concept:

The function is increasing if f'x>0 and decreasing if f'x<0.

2) Given:

F(0)=1

3) Calculation:

Since F(0)=1, (0, 1) is a point of F(x). Start from the point (0,1).

fx is negative when x0,2. Therefore, the F(x) is decreasing from (0, 1).

Notice f0=f2=0. So, F has horizontal tangent when x=0 & x=2.

For 2<x<3, f(x) is positive and increasing

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