Rolle's Theorem!!

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Want to understand Rolle's theorem in calculus? Look no further! In just under a minute, learn what Rolle's theorem states using graphs to gain a deeper understanding.

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The famous Rolle's Theorem. Something I feel I should still remember but don't.

HaldaneSmith
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i could have come up with that. but saying this is exactly what happened in XKCD 2042

trinityy-
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How to remember Rolle's Theorem: Imagine two cliffs of equal heights joined by a rope bridge suspended over the chasm. Now Rolle a bowling ball from one side and watch it roll back and forth until it comes to rest at the minimum height.

The bridge is the graph, the equal heights of the two cliffs means f(a) = f(b), and the ball comes to rest where f'(x) = 0. And if there's a gap in the bridge (the graph is discontinuous), then the ball won't come to rest at a minimum.

Next up: L'Hospital's Rule.

HaldaneSmith