Max and Min of Multivariable Function

To find the maximum and minimum value for the function f(x,y), we need to first find the critical points by taking the partial derivatives of f(x,y) with respect to x and y, setting them equal to 0, and solving for x and y. Then, we use the second partial derivative test or the determinant of the Hessian matrix to determine if the critical points correspond to a maximum, minimum, or saddle point.

The critical points for the function f(x,y) are the points where the partial derivatives of f(x,y) with respect to x and y are both equal to 0.

The second partial derivative test or determinant of the Hessian matrix is used to determine if the critical points correspond to a maximum, minimum, or saddle point for the function f(x,y).