Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 = 16

Given subject to the constraint

Let .

The gradient vectors of and are:

and

By Lagrange's theorem, there is a number , such that





It can be seen that has local extreme values at the given region.

X> -2 is the simplified version.