Rolle's Theorem
Description
To arrive at the Mean Value Theorem, we first need to understand Rolle's Theorem. Rolle's Theorem applies to functions on a closed interval, where the function is differentiable on the open interval, and where the value of the function at the endpoints of the interval are equal to one another. For functions of this type, Rolle's Theorem tells us that there is a point inside the interval where the slope of the function's derivative is equal to 0; in other words, where the slope of the tangent line is 0.
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5 min 11 sec
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