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...Wewill use this to prove rolle s theorem let a b if f is continuous on the closed interval and dierentiable open then there c in with that under these hypotheses has horizontal tangent somewhere between like local extrema ends proof of matter examining cases applying recall extremum either not at or since extreme value says maximum m minimum first we suppose so all values are equal constant x for one may take be anything example would suce weseek wish show keep mind...