Fall 2020 MATH 209 - Lab Quiz 2 1. (a) (2 points) Find the maximum rate of change of f(x, y) (3,4), and the direction in which it occurs. = In(x + y) at the point Po = (b) (2 points) Find the directional derivative of the function above at Po in the direction of =(3,}). 2. (3 points) Find the absolute extrema of the function f(x, y) =x+y=xy on the closed re- gion bounded by the triangle with vertices (0,0), (0, 4), (5,0) (so the edges of this triangle are segments of the lines x = 0, y = 0, and y = - fx + 4). - 3. (3 points) Use Lagrange multipliers to find the extreme values of the function f(x, y, z) 2x+2y+z under the constraint x + y + z = 4 =