Find the absolute maximum and minimum values of f (x, y) = x3 + y2 + 7 on the set D where D is the closed region bounded by y = 0 and y = 4 4x2. ' Part 1: Critical Points The critical points of f are: 2 ' Part 2: Boundary Work The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only submit your results for one of them. Along y = 4 4x2, f can be expressed as a function of one variable g(x) = f(x, 1 )= 2 List all the points on this side of the boundary which could potentially be the absoiute minimum or maximum on D. ' Part 3: Final Results Make sure you do the other computations along the other boundaries before you attempt this section! Find the function's absolute maximums and minimums and where they occur. The absolute maximum of f is: Z and it occurs at 2 The absolute minimum of f is: Z and it occurs at Z