5. Let f be continuous on [a, b] and differentiable on (a, b). Assume that m...

    

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5. Let f be continuous on [a, b] and differentiable on (a, b). Assume that m f'(x) M for all x = (a,b). Show that m+M 2 X am+bM 2 f(x) - (b)+ f(b) + f (a) m+M bm +aM X 2 2 2 for all x = (a, b). 5. Let f be continuous on [a, b] and differentiable on (a, b). Assume that m f'(x) M for all x = (a,b). Show that m+M 2 X am+bM 2 f(x) - (b)+ f(b) + f (a) m+M bm +aM X 2 2 2 for all x = (a, b).