Find and classify all mins and maxs of the

Question

Non-Linear Programming

1. Using Calculus, find and classify all mins and maxs of the function f(x,y) = 6 + x³ - 3xy + y³ on the region given by -3 ≤ x ≤ 3 and -3 ≤ y ≤ 3. Remember to check the boundaries.
2. Using the Solver, find all of the mins and maxs of the function f(x,y) = 6 + x³ - 3xy + y³ on the region given by -3 ≤ x ≤ 3 and -3 ≤ y ≤ 3.
3. Using Calculus, find and classify all critical points of the function f(x,y) = x² - 4xy² + 2x²y + 4 on the region given by -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2. Remember to check the boundaries.
4. Using the Solver, find all of the mins and maxs of the function f(x,y) = x² - 4xy² + 2x²y + 4 on the region given by -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2.

Note:  For each of the minima and maxima points found, please list the ordered pair, the function value at that point, and whether that point is a locally or globally-optimal point.