Calc04_2 - 4.2 Mean Value Theorem for Derivatives Teddy...

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Mean Value Theorem for Derivatives 4.2 Teddy Roosevelt National Park, North Dakota Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002

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If f ( x ) is a differentiable function over [ a , b ], then at some point between a and b : ( 29 ( 29 ( 29 f b f a f c b a - = - Mean Value Theorem for Derivatives
If f ( x ) is a differentiable function over [ a , b ], then at some point between a and b : ( 29 ( 29 ( 29 f b f a f c b a - = - Mean Value Theorem for Derivatives Differentiable implies that the function is also continuous.

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If f ( x ) is a differentiable function over [ a , b ], then at some point between a and b : ( 29 ( 29 ( 29 f b f a f c b a - = - Mean Value Theorem for Derivatives Differentiable implies that the function is also continuous. The Mean Value Theorem only applies over a closed interval.
If f ( x ) is a differentiable function over [ a , b ], then at some point between a and b : ( 29 ( 29 ( 29 f b f a f c b a - = - Mean Value Theorem for Derivatives The Mean Value Theorem says that at some point in the closed interval, the actual slope equals the average slope .

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