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

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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