A function f:A->A has convex/concave potential if there is F:R^n->R such that grad F=f, and F is convex/concave. Let A sub R^n be a compact set. Are there efficient ways to generate not trivial examples of such functions such that f:A->A is onto A ?

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
$f(x,y)=x^3-6xy+8y^3$

$\frac{1}{\sec <!--\; \; -->(x)}$ in derivative?

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