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Unformatted text preview: b. By hypothesis.jhas a derivativeat every interior point. That rules out (2), leaving us with interior points where f' = 0 and with the two endpoints a and b, If either the maximumor the minimum occurs at a point r: i:\side the interval, then f'(c) = 0 If both maximum and minimum are at a or b. then I is constant. f' = 0, and c can be taken anywhere in the interval. This completes the proof. )' tI (a) Discontinuous al an cndpoint No horizontal tangent. x y y = f(x) a (h) Disconlinuous at an interior point x y )' = f(x) It'. 1/ b (c) Continuous on [tI,//]bUI nol tlirrercnliahle al some inlcrior poinl...
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- Fall '08