Take f (x, y) = ax 2+by 2+cxy+dx+ey+t as an example.

Find the zero point of the partial derivative of f to x, that is, y=y 1, y2.

Find the zero point of the partial derivative of f to y, that is, x=x 1, x2.

List comparison

F (x 1, y 1), F (x 1, y2), F (x2, y 1), F (x2, y2) is enough.

If the domain of the surface is not infinite, use a linear function to find the extreme value of the boundary (you will), then find the extreme value as above, and compare the extreme values to get the maximum value.