Partial Derivatives--PLEASE HELP!

[MAM]

Find a point at which the surface given by F(x,y) = x² + 3x + y² - 4y + 7 is neither rising nor falling in either the x- or the y-direction.

 

[pappus]

Find a point at which the surface given by F(x,y) = x² + 3x + y² - 4y + 7 is neither rising nor falling in either the x- or the y-direction.

Use partial differentiation:

\(\displaystyle \displaystyle{\frac{\partial F}{\partial x} = 2x+3}\)
and
\(\displaystyle \displaystyle{\frac{\partial F}{\partial y} = 2y-4}\)

Both derivatives must equal zero. Solve for x and y. Plug in these values into F to get the value of the z-coordinate.

Check if you've found a maximum point or a minimum point.

For confirmation only I've attached the graph of the function.