1. The problem statement, all variables and given/known data Let some function, called f(u,v), be a differentiable function. Then, let its first partial with respect to u = 0 in some region, A. Then, for any u in the region A, f(u,v) will always equal itself for, let's say, f(ui, v) = f(uj, v). 2. Relevant equations 3. The attempt at a solution Alright, so it's obvious the function, f(u,v) really only depends on the variable v. The problem is then showing this, which I'm having a hard time doing. At first I tried to come up with a function f(u,v) that depends only on v but that didn't really fly. But if the first partial with respect to u equals zero, then isn't there no u-variable in the function? So wouldn't it be something like, f(u,v) = 2v^(2) or whatever? If u can't exist in the function, then a) How is it a multi-variable function? b) Does that prove or disprove that, say, f(ui, v) = f(uj, v)? Is there way to graph this? Obviously, I'm pretty confused.