In: Math
a) Let D be the disk of radius 4 in the xy-plane centered at the origin. Find the biggest and the smallest values of the function f(x, y) = x 2 + y 2 + 2x − 4y on D.
b) Let R be the triangle in the xy-plane with vertices at (0, 0),(10, 0) and (0, 20) (R includes the sides as well as the inside of the triangle). Find the biggest and the smallest values of the function g(x, y) = xy(20 − 2x − y) on R.