Hints for exam 3 review assignment, Calculus I,Spring 2009, Prof. Janeba
True-False quiz, p. 282, Stewart
1) Look at the graph of f(x) = x3 at x=0
2) See Fermat's theorem, section 4.1
3) See theorem 3 on p. 206 - what requirement isn't met in the quiz question? Now see the example in figure 7.
6) Investigate the graph of f(x) = (x-2)4, be sure to check the concavity on either side of 2, and look up the definition of an inflection point.
7) f and g have the same derivative, so f and g are both antiderivatives of the same function. Does a function have only one antiderivative?
19) If f(1)=f(0), then what would Rolle's theorem say (p. 214)
Exercises, p. 282-284, Stewart
13) Don't worry about the limits (they'll give some asymptotes), just get the rest of it right.
17,21,25) For "guidelines", let's use: Tell where the function in
incresing & decreasing, and where it has local extrema (of what
kind?), and where the function's graph is concave down, concave up, and
where it has inflection points.
29) You have to compute f ' and f '', but note the emphasis on graphing them. (This isn't really any different than the way we've always done these problems.)
49) "Revenue" means the amount of cash that comes into the ticket
office. Expenses aren't considered here, just the income.
63) Remember that in the metric system, gravitational acceleration is constantly 9.8 m/sec2. Use some antiderivatives.
65) Find the maximum cross-sectional area; they're just giving you the answer in advance.
Last Modified April 27, 2009.
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