critical point for f(x,y)=x+y?

from the wiki:

For a differentiable function of several real variables, a critical point is a value in its domain where all partial derivatives are zero. The value of the function at a critical point is a critical value.

The partial derivatives for this function of 2 variables, f, at an arbitrary point (x,y) is:

∂f/∂x = 1

∂f/∂y = 1

So the partial derivatives are nowhere zero and so cannot be zero simultaneously.

So no critical points exist for this function.

f(x,y) = x + y

fx = 1

fy = 1

no critical point

There are none, it's a plane.