Find a vector giving the direction in which the function f increases most rapidly at the point P. What is the maximum rate of increase? (a) f(x, y) = 2x+3y, P = (3,2) (b) f(x, y) =e-2x cosy, P = (0,4) The figure shows a topographical map of a 620 m hill with contours at 100 m intervals. (a) If you start from A and proceed in a southwesterly direction, will you be ascending, descending, or neither as- cending nor descending? What if you start from B? (b) If you start from C and proceed in a westerly direction, will you be as- cending, descending, or neither as- cending nor descending? D A 620 600 500 400 300 W--E 200 (c) If you start from D, in what direction should you proceed to have the steepest as- cent? (d) If you want to climb to the summit of the hill using the gentlest ascent, would you start from the east or the west?