Question: Problem 1(25 pts) Consider f(x) = x 3 6x 2 + 9x + 4 defined on R. (i) Find all critical points and inflection points

Problem 1(25 pts) Consider f(x) = x 3 6x 2 + 9x + 4 defined on R.

(i) Find all critical points and inflection points of f, find and classify all local extrema of f.

(ii) Sketch the graph of f.

(iii) Is f convex or concave on R? More generally prove or disprove the following result: There exists a, b, c, d such that cubic function ax3 + bx2 + cx + d is convex on R. Here a not = 0.

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