Please provide the full solution thansk!

Consider the surface = = f(x, y) = e- (x + 3)2 + 2y?). A small portion of the surface, displaying its major features, is shown below in the contour plot on the left. On the right is a magnified section of the contour plot overlayed with a semi-circular region whose boundary (solid red line) is formed by the intersection of a2 + y? = $ and y = -2x. 1 10/ 89670ed 20 1.5 -2027 2 23.675 13 6 16.9 -10.2 $5.5 $2 1 1.0 -18.7 15.3 0.5 - 10 0.0 - -0.5/ -1 -1054 5.5 - 2 P7060 10 -1.5 2823 2,23421 18.71 45 3136 -4 -3 -2 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 (i) (a) On the unconstrained (open) domain, find any critical points of f. Compute the value of the function at these points. (b) Characterise each critical point using the second derivative test. (ii) Determine which, if any, of the critical points from (i) are in the semi-circular region R. (iii) Compute the points of intersection of the two curves and compute f at these vertices