3. Prove or provide a counterexample for the following: (a) Let f: Rn → Rm and g : Rm → Rk. Suppose all directional derivatives of f and g exist at a point pe Rn and f(p) = Rm respectively (Dvf(p) and Dug(f(p)) exist for all v R and u € Rm). Then all directional derivatives of g of exist at p. (b) Let SCR be open and f: S→ Rm. Suppose that all partial derivatives are bounded on S. Then f is continuous on S.

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