Question

What are the values and types of the critical points, if any, of `f(x,y)=2x + 4y + 4`?

Answer 1

That function has no critical points. (It is a plane.)

Explanation:

`f_x(x,y) = 2` and `f_y(x,y) = 4`.

It is not possible to make the first derivatives undefined or zero. So there are no critical points.