1. Let f(x,y) = x +zy -xy +2 and R= (x,y)x3 +y'

1. Let = x 2 -F} Y2 xy2 +2 and R = + y 2 < 4} . (a) (8 pts) Find fx and fy . (b) (12 pts) Find all critical points of f on the interior of R . List them as ordered pairs. (c) (8 pts) Consider the boundary of R , the circle where y = 4 x2 a function of only x. Represent f restricted to the boundary as (d) (16 pts) Find the critical points on the boundary of R . List the x- and y-coordinates.