Question 1. For each set of conditions below, give an example of a function f that satisfies the given conditions; you should give the graph and formula for each function explicitly, and show that your function satisfies all the conditions in each part. (You may use piecewise-defined functions if needed.) (a) A function f that is strictly increasing on (-00, 0), strictly decreasing on (0, ∞o), and is concave up everywhere (except possibly at x = 0). (b) A function g that is twice differentiable, has exactly two inflection points, and exactly one local maximum point.

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