The function are  and .

Find .

Apply the General Power Rule for Integration:.

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(a) Graph the functions and in a same viewing window.

The functions are and .

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(b) Explain why  is nonnegative.

is nonnegative because the graph of is positive at the beginning, and generally has more positive sections than negative ones.

(c) Identify the points on the graph of that correspond to the extrema of .

The points on that correspond to the extrema of are points of inflection of .

(d) Does each of the zeros of correspond to an extremum of .

Explain.

No, some zeros of , such as , do not correspond to extrema of .The graph of continues to increase after because remains above the -axis.

(e) The function .

Consider

Apply limits .

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Substitute and in aboove expression.

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Graph the function: .

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Observe the graph:

The graph of  is that of is shifted  units downward.

(a) Graph of the functions and in a same viewing window.

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(b) is nonnegative because the graph of is positive at the beginning, and generally has more positive sections than negative ones.

(c) The points on that correspond to the extrema of are points of inflection of .

(d) No, some zeros of , such as , do not correspond to extrema of .The graph of continues to increase after because remains above the -axis.

(e) Graph of the function: .

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