Calc04_2 - Mean Value Theorem for Derivatives 4.2 2 2-∞ 1 ae è ø È 1,¥ ae è ø 3 3 é ê ù ú 3 3 é ê ù ú 3 3 ae è

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Unformatted text preview: Mean Value Theorem for Derivatives 4.2- 2 , 2 ( )-∞ ,- 1 ae è ç ö ø ÷ È 1,¥ ae è ç ö ø ÷- 3 , 3 é ë ê ù û ú- 3 , 3 é ë ê ù û ú- 3 , 3 ae è ç ö ø ÷ C = -5 If f ( x ) is continuous over [ a , b ] and differentiable over ( a , b ), then at some point c between a and b : ( 29 ( 29 ( 29 f b f a f c b a- ¢ =- Mean Value Theorem for Derivatives The Mean Value Theorem only applies over a closed interval. → The Mean Value Theorem says that at some point in the closed interval, the actual slope equals the average slope . y x A B a b Slope of chord: ( 29 ( 29 f b f a b a-- Slope of tangent: ( 29 f c ¢ ( 29 y f x = Tangent parallel to chord. c → Example Explain why each of the following functions fails to satisfy the conditions of the MVT on the interval [-1,1]: 3 2 2 x +3, for x < 1 a) f(x) = x + 1 b) f(x) = x + 1, for x 1 ≥ f(x) = x + 1 which is not differentiable at (0,1) lim x →1- φ(ξ29 = 4, λιμ ξ→1 + φ(ξ29 = 2 Σινχε τηεσε λιμ ιτσαρε νοτεθυαλ , φ(ξ29...
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This note was uploaded on 02/16/2012 for the course CALCULUS 0064 taught by Professor Waldron during the Fall '10 term at Broward College.

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Calc04_2 - Mean Value Theorem for Derivatives 4.2 2 2-∞ 1 ae è ø È 1,¥ ae è ø 3 3 é ê ù ú 3 3 é ê ù ú 3 3 ae è

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