Problem 1: For each of the following, answer True or False. Give a one sentence justification or a counterex- ample; a counterexample requires no additional justification or explanation. (d) There exists a three-times differentiable function such that f > 0, , f' < 0, f" > 0, and f" <0 (for all x e R). (e) If gof is injective, then f is injective. (f) Suppose f(x) is positive, increasing, concave up, and defined on [0, 1]. Then the volume of the solid of revolution obtained by revolving f around the y-axis is larger than the volume of the solid of revolution obtained by revolving f around the x-axis.

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