# Mean Value Theorem & Geometric Consequences

## Mean Value Theorem

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The Mean Value Theorem is briefly defined.

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Definition and explanation, including Rolle's Theorem.

Eight questions which involve showing or proving statements using the Mean Value Theorem, including a question about speeding on the Massachusetts Turnpike.

Stating the theorem and using it to prove two statements about functions.

Using the theorem to justify two statements.

Using the theorem to place an upper and lower bound on a function value.

## Application of the Mean Value Theorem

Mean Value Theorem used to solve error analysis problem involving the precision of a device's signal output.

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## The Mean Value Theorem Revisited

Review of Mean Value Theorem, with introduction of Generalized Mean Value Theorem.

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## Accuracy of Approximations, and the Mean Value Theorem

Finding the error in an approximation of a function, leading to the Mean Value Theorem.

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