Let f(x, y) = { y^3 / (x^2 + y^2) if (x, y) != (0, 0), 0 if (x, y) = (0, 0) a) Using the definitions of partial and directional derivatives, evaluate fx(0, 0), fy(0, 0) and Duf(0, 0) where u is the direction of i + j. b) By Sertoz' Theorem, the function f(x, y) is continuous at (0, 0). Is the function f(x, y) differentiable at (0, 0)? (Justify your answer.) Determine the set of critical points of the function g(x, y) = x sin(x) + cos(x) - y sin(x) + y^2/2. (Explain carefully your solution; you can use freely the fact that t = 0 is the unique solution of the equation sin(t) = t.)