1. (a) Draw the graphs of the functions x and x in the plane. Then find all integers n > 2 such that (0, 0) is an inflection point of the function f(x) = x". (b) The second derivative f" of ƒ is given by f"(x) = (x + 1)®x°(x – 2)^(x – 4)³ for all r. Find all a corresponding to inflection points of the graph of f. (c) A polynomial function g has degree 18 (like the degree of f" in part (b)). What is the maximum number of inflection points that the graph of g could possibly have? Explain your answer.

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