Math 202 Written Homework 12 (14.2, 14.3) Write neatly. Always give enough work and clear explanation. This assignment has 30 possible points, but it will be weighted as 15 maximum points in the gradebook. 1. For the function z = f(x,y) = 3xZy* + -4 -5x, find the following. Simplify your answer. a) [4 pts] fx(x,y) azz b) [6 pts] aydx (2,-1) 2. [10 pts] For the function given below, find all critical point(s). Show your work clearly. f (x, y) = x* - 2xy + 2y2 3. [10pts] The function f(x, y) = 2x* + 4y? - 24xy has three critical points, (-3, -9), (0,0) and (3, 9). Use the Second Derivative Test from 14.3 to classify each critical point as coordinates of a local minimum, local maximum or saddle point. Show your work clearly. o Find all appropriate partial derivatives here: Show work and answer for point (-3, -9): o Show work and answer for point (0, 0): o Show work and answer for point (3, 9)