   Chapter 3.9, Problem 52E

Chapter
Section
Textbook Problem

# Draw a graph of f and use it to make a rough sketch of the antiderivative that passes through the origin.52. f ( x ) = x 4 − 2 x 2 + 2 − 2 , −3 ≤ x ≤ 3

To determine

To sketch: The graph of the function f(x)=x42x2+22,3x3 and sketch the rough graph of the antiderivative function F for the function f(x)=x42x2+22,3x3

Explanation

The given function is an even function.

Use the equation of function f(x)=x42x2+22,3x3 and sketch the graph of the function as shown in Figure 1.

Thus, the graph of the function f(x)=x42x2+22,3x3_ is sketched.

The antiderivative function passes through the origin.

Refer to the Figure 1 in Part (a) for the graph of the function f(x)=x42x2+22,3x3 .

As the graph of the function f(x) is an even function, the antiderivative function is an odd function

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