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