1. The problem statement, all variables and given/known data In general, I've been given a few functions of two variables, x and y. I have been asked to find all critical points by setting the gradient of the function equal to 0. Further we are asked to classify these critical points using some given rules regarding the Hessian matrix. 2. Relevant equations 3. The attempt at a solution For example, I'm given [itex] f(x,y) = x^4 + y^4 − 4xy + 1 [/itex] By solving the gradient equation, I got the fixed points (0,0) , (1,1) , and (-1,-1). When I look at the Hessian matrix evaluated at either (1,1) or (-1,-1), the Hessian is the same and is positive definite. From this I conclude that both (1,1) and (-1,-1) are local minima with f(1,1) = f(-1,-1) = -1 How can I show that this is also a global minimum?