Let f (x, y, z) = xy - xyz + z. (a) What is the maximum rate of increase of the function at the point (1,2,1), and in which direction does it occur? (b) Find the directional derivative of the function f at the point (1,2,1) in the direction with direction angles 60, 45 and 60. Q4)(20 points) Find the plane tangent at the point (2,3,-1) to the surface defined implicitly by the equation In(xy + x2 + yz) = 0 assuming z = f(x,y) is a differentiable function of x and y in some neighborhood of the point (2,3). and z = -1 when x = 2 and y = 3.