3.2 Mean Value Theorem

# 3.2 Mean Value Theorem - Geometrically the mvt guarantees...

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Mean Value Theorem Section 3.2

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Rolle’s Theorem
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 - - ) ( ) (

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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

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Unformatted text preview: 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? poly-no-mial What do you get if you divide the circumference of a jack-o-lantern by its diameter? pumpkin “pi” What are eyeglasses good for? di-vision...
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3.2 Mean Value Theorem - Geometrically the mvt guarantees...

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