Consider the function f : R2 → R, ={* (r, u) + (0,0) (x, y) = (0,0) f(x, y) 0, (a) Argue that f is differentiable on R²\{(0,0)} and compute f, and fy away from the origin. (b) Check that f is continuous at (0, 0) (and hence everywhere). (c) Check whether all directional derivatives Dy f(0,0), v = (v1, v2), exist at (0,0). In particular, check if either of the partials f-(0,0) and fu(0, 0) exist. If your answer is "yes", find the respective derivative.

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