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Unformatted text preview: critical number in (a,b), but it may not yield a horizontal tangent. a c b The Mean Value Thm. If f is continuous o the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a # c in (a,b) such that f ‘ (c) = a b a f b f) ( ) ( Why is it called mean? At some point, instantaneous rate of change = average rate of change (a,f(a)) (b,f(b)) f ‘ (c) c slope of tangent line = slope of secant line Geometrically, the mvt guarantees the existence of a tangent line that is parallel to the secant line through the points (a, f(a)) and (b,f(b)). Joke Time What would a math student say to a fat parrot? polynomial What do you get if you divide the circumference of a jackolantern by its diameter? pumpkin “pi” What are eyeglasses good for? division...
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 Fall '08
 JARVIS
 Calculus, Derivative, Mean Value Theorem, #, Rolle, Mean Value Thm

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