1. (a) (2 points) Find the maximum rate of change of f{;'i:,y) : ln(:.l:2 + yg) at the point. P" = (3. 4). and the direction in which it occurs. {h} (2 points) Find the directional derivative of the function above at PE] in the direction of Qt}: (599- 2. {3 points) Find the absolute extrema of the function f ($.35!) = :I:+ g; my on the closed re gion bounded by the triangle with vertiees ((1,0), ([1, 4). (5, (I) (so the edges of this triangle are segments of the lines :1: = (J, y = U, and y = Err: + 4). 3. (3 points) Use Lagrange multipliers to nd the extreme values of the function 3' (11.35:, 3) = 2:1: + 23; + 2: under the constraint 3:2 + 312 + 22 = 42