4. (1 Point) Quick Multiple Choice/Short Answer (a) The Method of Lagrange Multipliers is useful for optimizing a function f(x, y) relative to a constraint g(r,y) = c. The method is based off of the idea that at extreme values, the gradients Vf and Vg are... (mark one) O Parallel O Orthogonal O The same length O None of these (b) True or False: Every Lagrange Multiplier problem is guaranteed to yield both a minimum and a maximum. O True O False (c) On the graph below are the level curves of a mystery function f(x,y), sketched in black. There is also a constraint curve g(x, y) = 8, sketched in blue. Use this contour map to estimate the maximum and minimum values of f(r, y), subject to the constraint g(r, y) = 8. No justification required. 8 9 10 6 6 8 > 4 7 3 2 2 O 5 2 6 8 X Max value: Min value