- #1

tracedinair

- 50

- 0

## Homework Statement

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(u

_{i}, v) = f(u

_{j}, v).

## Homework Equations

## 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(u

_{i}, v) = f(u

_{j}, v)?

Is there way to graph this?

Obviously, I'm pretty confused.