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Let f : 1R2 > R be a function such that all the directional derivatives at 0 exist. The following parts are independent. (a) If all the directional derivatives of f at 0 are the same, prove that all of them are equal to 0. (b) If f is differentiable and all the directional derivatives of f at 0 have the same absolute value, prove that all of them are equal to 0. (0) Give an example of a function f such that all the directional derivatives of f at 0 are $1