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Problem 4: The plane x = 1, intersects the paraboloid at z = x2 + y2 in a parabola. Find the slope of the tangent to the parabola at (1, 2, 5). (Ans: 4) i. Problem 5: Find the directions in which the functions increases and decreases most rapidly at P0, respectively. (or nd the directions in which the directional derivative is maximum and minimum, respectively). (a) f(x,y) = x2 + xy + yz, Pu(1,1) (Ans: max 3/5, min x/) (b) f(x, y) = xzy + ex? sin y, at P0 (1,0) (Ans: 2, 2) Problem 6 In What direction is the derivative of f (x, y) = xy + y2 at P(3,2) equal to zero