4. Determine the maximum rate of change of f at the given point P and the direction in which it occurs (a) f(x,y) = sin(xy), P(1,0) (b) f(x,y,z) = P(8,1.3)
5. Show that a function f decreases most rapidly at x in the direction opposite to the gradient (that is, in the direction of −∇f(x)) and that the maximum rate of decrease equals −|∇f|