Question: a) Over what region is the function f (x) = x 3 convex? Over what region is f concave? b) Over what region is the

a) Over what region is the function f (x) = x ³ convex? Over what region is f concave?

b) Over what region is the function f (x) = 12x + x ³ convex (concave)?

c) Plot the function f (x) = 12x + x 3 over the region 3 x ³. Identify local minima and local maxima of f over this region. What is the global minimum and what is the global maximum?

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