Question: 5. Let f R2 R be a function defined by x+ y if y0; y f(x, y) = if y = 0. (a) Show

5. Let f R2 R be a function defined by x+ y if y0; y f(x, y) = if y = 0. (a) Show that all directional derivatives of f exist at (0,0), i.e. Vvf(0,0) exists for any unit vector v R. (b) Show that f is not differentiable at (0,0). (c) Find gradient vector Vf (0, 0). Is it true that Vf(0,0) v=Vvf(0,0) for any unit vector v R?

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