Let f:[0,1]->[0,1] be a strictly increasing continuous concave function with f(0)=0 and f(1)=1. Let g be the inverse of f. Then g is strictly increasing and convex.It seems that the function h(x)=f(1/2g(x)) is always convex. Is this true? If yes, why?

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

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