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**Unformatted text preview: **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 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. 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...

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