This is not a homework question.
Just wondering if there is a general formula for the gaussian curvature at point (x,y,f(x,y)) in terms of x, y, and f(x,y).
I didn't see any thing like that on the wikipedia article, but maybe it's hidden behind all these letters/symbols which are not actually described.
By the way, I'm studying computer science. For us, a general formula is one that works most of the time. When it doesn't work, we call this an exception, and it requires special handling :). So here of course, the function is assumed everywhere indefinitely continuous and differentiable and bounded inside any box that would fit the RAM - whatever that means - and also in R3, inside a standard classical euclidean space...