Problem Solutions: 4.6

Problem #1, p. 276: The first derivative has zeros at three points (it's a cubic, and can have at most three zeros, or roots): approximately at -1, 1/3, and 3/4:

The second derivative has two roots (as a quadratic, it has at most two): approximately at plus or minus .6:

Hence, the action is occuring between -1.5 and 1, say, with three max/mins, and two inflection points:
Problem #10, p. 276:
After playing with the window of f, I found a good interval to plot was on [-20,20], with a range of [-4,4]. This shows the roots, the asymptotes, the inflection point, the intervals on which we're increasing and decreasing, etc.:

Analysis of the function's derivatives shows that there is a root of th derivative at 40/11, and a root of the second derivative at 60/11. The horizontal asymptote is the line y=1.

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