Part (a) Sketch and describe the surface z = f (x, y) where f (x, y) = (x - 2)2 + (y -2)2. Part (b) Consider the function f (x, y) = x*y. (i) Calculate the gradient vector V f (x, y) of the function f (x, y). (ii) What is the magnitude of the greatest rate of increase of f (x, y) at (-1, 2)? What is the direction of the greatest rate of increase? (You may use a vector in the cy plane to specify this direction. It does not have to be a unit vector.) Part (c) Consider the second-order differential equation dar2 + 8- dy + 25y = 0. dx Find the general solution of the equation. (ii) Use the general solution from part (i ) to evaluate lim y (x). (iii) Find the particular solution which satisfies y(0) = 3 and y'(0) = -2