Please provide the full solution thanks!

Consider the surface 3 = f (1:, y] = e'm (a: + 3]2 + 2312]. A smail portion of the surface, displaying its major features, is shown below in the contour plot on the left. On the right is a magnied section of the contour plot overlayed with a send-circular region whose boundary (solid red line) is formed by the intersection of 1:2 + y2 =i and y = 2:v. (i) {a} 0n 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 serni-circular region R