The function are  and .

Find .

Apply the General Power Rule for Integration:.

.

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

The functions are  and .

(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 .

.

Substitute  and  in aboove expression.

.

Graph the function: .

Observe the graph:

The graph of  is that of  is shifted  units downward.

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

(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: .

.