Rolle's Theorem on Scientific American

Good to see the little remembered Rolle's Theorem in Scientific American. A Proof of the Math Fact of Rolle in Short Words. Yes, if you have taken calculus, you have seen it.

The title suggests a short quick proof, oh the challenge is using just in one-syllable words. It still can be longer and more complex than it should be in one syllable words?

Now the Rolle's Theorem actually says something SIMPLE. See this picture again.

Look, in x-axis. mark two positions a and b. Then draw a line from a to b (without going backward or lifting your pen, or you mess the meaning of a function or mess with the requirement being continuous). To land on b, you must have a point c where you are at the highest point or the lowest point, that's when derivative = 0. Or you can do a flat line in which everywhere derivative = 0, in which everywhere is a c.

Ok, what I just mentioned is informal. The language of math requires more formal. Don't like it? Well going to a formal party requires a tuxedo too.

This one is easy to visualize. Why bother make a theorem for this? Because we need to name it as a step to prove something not as obvious.

What's the big deal of Rolle's Theorem you say? It is "a special case" or it can be extended to become the "Mean Value Theorem".. which is a crucial step needed for the Fundamental Theorem of Calculus.

Oh and such British accent to say naught. Isn't that supposed to come from Scientific American?