Let f:R_(>=0)->R_(>=0), and g:R_(>=0)->R_(>=0) be two functions. Suppose that f(0)>g(0)=0, and f is strictly increasing and concave, while g is strictly increasing and strictly convex (so f′(x)>0,f′′(x)<=0,g′(x)>0, and g′′(x)>0). Suppose that for some x>0 we have that f(x)−g(x)>0. Is it true that then for every y in [0,x] it must be that f(y)−g(y)>=0?

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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