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...The mean value theorem astudent at university of connecticut happens to be travelling boston he enters massachussetts turnpike sturbridge village entrance in morning since uses fast lane never actually picks up a ticket but sensors record that goes through toll newton just minutes later soon receives trac summons mail indicating vi olated posted speed limit and decides appeal there is no indication was caught by radar appearingincourt theprosecutorarguesthathetravelled miles therefore travelled an average per hour more than above highest thestudent argues although may have averaged evidence ever instantaneous judge considers arguments quickly rejects student s plea noting implies his aver age had least one instant during which rolle stheorem suppose function f continuous on closed interval dierentiable open b then number c such geometrically this says if are two points smooth curve takes same height must point between where tangent horizontal special case proof satises hypotheses extre...