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8-35.

Is there a in the interval for where ? Justify your answer.

If is continuous AND differentiable on the given domain, then the Mean Value Theorem will apply.

The Mean Value Theorem

The Mean Value Theorem for Integrals

If   is continuous on , then there exists at least one point  in  such that                     .

The Mean Value Theorem for Derivatives

If  is continuous on  and differentiable on , then there exists at least one point  in  such that .