Apply Rolle’s Theorem and the Mean Value Theorem and their geometric consequences.

Example Problems
Let and let c be the number that satisfies the Mean Value Theorem for f on the interval .

What is c?
Estimating using a Maclaurin polynomial, what is the least degree of the polynomial that assures an error smaller than ?
Estimating using a Taylor polynomial about , what is the least degree of the polynomial that assures an error smaller than ?
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