Rolle's Theorem

Good ole' Michael Rolle...do you know that Rolle once argued AGAINST the use of calculus.  In fact, he even wrote a critique of calculus that was NOT very flattering.  Luckily, he came around and gave calculus one of its most useful theorems: Rolle's Theorem

While doing your Rolle's Thm HW (pg. 267, 3-8) remember you must show THREE things:

1. That the endpoints are EQUAL.  Plug your left and right hand endpoints into the original f(x) to show this.
2. You must show (or at least say) that f(x) is continuous and differentiable on the interval between [a,b].
3. Find the derivative,set equal to zero, and verify that that point exists and is in between a and b.  (if a and b are your endpoints)

Rolle's Theorem & Example

Check out video below for help on a couple of HW problems and a sweet quote from Michael Rolle himself (thanks Grant):