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

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Answer 1 · 2016-08-09T20:42:07

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

$f_{x} (x, y) = 2$ $f_x(x,y) = 2$ and $f_{y} (x, y) = 4$ $f_y(x,y) = 4$ .

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

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