Local Extreme Values and the Mean Value Theorem Part 2 - Consequences of the Mean Value Theorem
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Local Extreme Values and the Mean Value Theorem Part 2 - Consequences of the Mean Value Theorem
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This episodes focusses on the mean value theorem and its consequences. One way of describing the mean value theorem is that the average velocity must be attained at some point. Reading this fact somehow backwards tells us some thing about the average velocity given some information about the derivative. Indeed, monotonicity can be obtained if the derivative has only one sign; also a sufficient criterion for the existence of extreme values can be shown. Other consequences like the generalised mean value theorem of the theorem of Bernoulli—l’Hospital are mentioned; for the precise statements we refer to the lecture noted however.
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