Suppose the temperature (measured in F) in the elliptic ball = {(,,): ²+4²+² 4} is given by (,,)= ²2+²²+70.

a) Sketch the region of W and find and classify the critical points of that are located in the interior of .

b) On your sketch of the region , draw the meridional curve given by ()=(0,cos(),2sin()) ,[0,2]. Now, use the parametrization above to determine the maximum and minimum temperatures registered on . At what points are those temperatures attained?

c) By looking at the points you found in (a) and the ones you obtain from applying the method of Lagrange multipliers to the boundary of , determine the maximum and minimum temperatures registered in the entire region . At what points are those temperatures attained?