Problem 1 (20 marks) Let f: (a,b) R be continuous. Prove that given x, xz, x, xn Ela,b), there exists X E(a, b) such tha

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Problem 1 20 Marks Let F A B R Be Continuous Prove That Given X Xz X Xn Ela B There Exists X E A B Such Tha 1 (57.37 KiB) Viewed 36 times

Problem 1 (20 marks) Let f: (a,b) R be continuous. Prove that given x, xz, x, xn Ela,b), there exists X E(a, b) such that noffel= for It ffice) tuit floud. Problem ? (30 marks) Let of be continuous on [a,b] and differentiable on (a, b). Prove that if azo, then there are X1, X2, Xs e Cabo Sancle that f')= (bta) fixa) = (1+ba+as) fiets? 3x3 Suppose f exists and is bounded on (0,0). Prove that if bin f6)=0, then lin f(x) = 0. Problem 4 (20 marks) Let fand og be functions Continuous on [a, b], differentiable on the open interval (a, b) and let f(a)= f(b) = 0. Show that there is a point X E (a, b) such that o'x) fox) + fá)=0. f'x Problem B (30 marts 222 X X