Problem 5: [20 pts] A contour plot for a differentiable function f{:r, y} is shown below. The value that z : f(o:, 3;) takes along each contour is listed; for instance f[B) : 3. Additionally, f(3:, y) either strictlyr increases or decreases between contour lines and Vf 79 0 at Points A, B, 01 or D. A. [5 pts] (Select All): Indicate at which points, if any, the following conditions hold. You do not need to justify your responses. 0 [2.5 pts] At which of points below is g > I]? 3y @ Point A. Point B. Point 0. Point D. o [2.5 pts] At which of the points below is g 0? Ba: @ Point A. Point B. Point C. (1) Point D. 1 4 B. [5 pts] Find Vf (0,0) or state what additional information would be needed to determine it. Hint: One way to proceed is to recall the important relationship between the gradient and level curves and what can be deduced based on the picture. [Pm Hem. .5, continued) The curve traced out from left to right by a differentiable vectorvalued function pm is shown below on the contour plot of at, 3;) from the previous page. For the rest of this problem 36) refers to this parameterization. C. [6 pts] Harper is asked to consider % [f (330] at the point A (or, written more succinctly, $04))\" Explain to Harper whether it is possible that 011) : 0. If it is possible that gun 75 I], explain whether %(A) should be positive or negative. 15 D. [4 pts] Taylor claims that at Point A, the curve traced out by ft) in the above image could point in the direction ii in which Df(A) is maximized. Determine if Taylor is correct and explain your response