Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem
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Local Extreme Values and the Mean Value Theorem Part 1 - Rolle’s Theorem
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Having defined the derivative of a function in the previous episode, we now turn to properties of the derivative and of the function in connection to the derivative. This episode is concerned with a first theorem asserting as much, namely Rolle’s theorem. This theorem tells us that the derivative of a differentiable function has a zero as long as it assumes one value twice. A consequence of this will be the mean value theorem, the consequences of which we address in the next episode.
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