Need help with this constrained optimization problem for multivariable calculus please

. (2 points) Suppose you generate the following Python plot showing a contour map for f (x, y). Let S be the set of points satisfying the inequality $2 + y2 S 9. (a) (1 point) Suppose that f (3mm, gum\") is the global maximum of f (:13, 3;) on the set S. Circle the TRUE statement. The point (rmz, gm\") is on the boundary of S in Quadrant I in the interior of S in Quadrant I on the boundary of S in Quadrant II in the interior of S in Quadrant II on the boundary of S in Quadrant III in the interior of S in Quadrant III on the boundary of S in Quadrant IV in the interior of S in Quadrant IV (b) (1 point) Suppose that f (rm-n, gym-n) is the global minimum of f (r, 3;) on the set S. Circle the TRUE statement. The point (mm-n, ymm) is on the boundary of S in Quadrant I in the interior of S in Quadrant I on the boundary of S in Quadrant II in the interior of S in Quadrant II on the boundary of S in Quadrant III in the interior of S in Quadrant III on the boundary of S in Quadrant IV in the interior of S in Quadrant IV