À differentiable function f: (a, b) → R is uniformly differentiable on a, b if for every E>0 there exists a d > 0 such that | f(t) – f(x) く€ t - I or all t, r E [a, b] with 0< t- x| < 6. Show that f is uniformly differentiable on [a, b] E and only if f' is continuous on a, b.

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