(a) Let f: R → R be a differentiable function such f(tx) = tf(x) for all t ≤ R, x € Rª and some fixed me N. Show that: n [ i=1 af Xi ¹Jxi = mf(x) = Hint: Consider the function g(t) = f(tx) and g'(1) (b) Let f: Rn → R be a non-linear function such that f(tx) = tf(x) for all t = R, x ER". Show that f is not differentiable at 0.

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