Find the absolute minimum and maximum values of f on the set D, where f(x,y) = 2x3 + y4, D = {(x,y)|x2 + y2 1}. To complete this problem, use Matlab for parts a) and b).

(a) Use Matlab to draw the contour map of f and the curve g(x,y)=x2+y2-1=0 on the same figure.

(b) Looking at the graph Matlab produced, predict where are the critical points of f restricted on the constraint g = 0. Explain your reasoning.

(c) Find the critical points of f inside of D.

(d) Use Lagrange Multipliers to nd the critical points of f along the boundary of D. To do this, dene h(x,y) = f(x,y)g(x,y).

(e) Based on your calculations above, nd the absolute minimum and maximum value of f and the points at which they occur.