Consider the surface z = f(x, y) = e- ((x + 3)2 +2y2). 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 x2 +y? = ; and y = -2x. 1 10 8907060 73d 20 1.5 -2827 2'23.8 20.N -3 2 /5 'V5 1.0 18.7 15.3 0.5 - 10 0.0 - 85 6.8 -0.5- -1 -1.0 10.4 215 -2 1 106807080 50 40 10 -1.5 2823 2 23221 18.714 45 3136 -2 .1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 (i) Let B2 represent the semi-circular boundary x2 + y = 2. Compute to and ty if B2 has the anti-clockwise parametric definition r(t) = , cos(t)i + , sin(t)j te (to, tf). Use the total derivative = Vf . it " to find any critical points on B2 and compute f at these points. of = (e *(-x2 -4x - 3) )it (Aye *)