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Can you explain Rolle's Theroem? How do you apply it in your work?

Explain Rolle's Theroem #math #theory #calculus #ap-calculus

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Abe’s Answer

One of the good explanations of Rolle's theorem is on Wikipedia (https://en.wikipedia.org/wiki/Rolle's_theorem). In a nutshell, the theorem says that for a continuous and differentiable function that has equal values at the end points of an interval [a,b], the derivative must be zero somewhere in that interval.

The key is continuity and differentiability. A function is continuous if intuitively you can draw the function without lifting the pen, and differentiable if the derivative is defined and varies smoothly within the interval.