Problem 4: (5 points) The plane x = 1, intersects the paraboloid at z = x2 + y in a parabola. Find the slope of the tangent to the parabola at (1, 2, 5). (Ans: 4) Surface Plane Tangent (1. 2. 5) line Problem 5: (10 points) Find the directions in which the functions increases and decreases most rapidly at Po, respectively. (or find the directions in which the directional derivative is maximum and minimum, respectively). (a) f(x,y) = x2 + xy + y?, Po(-1,1) (Ans: max v2, min -V2) (b) f(x, y) = xy + exy siny, at Po (1,0) (Ans: 2, -2)