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  3. 4 consider a function f that is differentiable on an...

Question: 4 consider a function f that is differentiable on an...

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4. Consider a function f that is differentiable on an open inetrvet (a, b). (a) Suppose that f is bounded on (a,b), i.e suppose that there exists K R such that If (x) K for all E (a, b). Prove that If (x) - f(u)l s K y for all r,y e (a, b). (We say that f is Lipschitz.) (b) Prove that a Lipschitz function on (a, b) is uniformly continuous on (a, b).
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