# Rolle's Theorem: Practical Applications

#### brewAP2010

1. The problem statement, all variables and given/known data
I know that Rolle's Theorem states that if the function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), and if f(a)=f(b) then there is at least one number c in (a,b) such that f'(c)=0. I want to know if there are any practical applications for Rolle's Theorem?

2. Relevant equations

3. The attempt at a solution

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#### micromass

Not really. Rolle is more of an intermediate theorem. It helps to prove Taylor theorem (which is very applicable), the mean-value theorem abd the exreme-value theorem.

But Rolle's theorem by itself. I don't really see many practical applications that aren't far-fetched...

#### harp AP 2010

Rolle's theorem is basically the mean value theorem, but the secant slope is zero. Therefore, Rolle's theorem is interchangeable with mean value and an application of it would be:
to prove a vehicle was speeding along a 2.5mi road where the speed limit is 25mph but is seen going below the limit on the ends of the road but the time between the readings is 5 min. Going the speed limit the fastest time you can take is 6 mins (6/60)(25)=2.5. 5<6 proves he was going over the speed limit at least once(probably twice).

ok thanks a lot

#### hgfalling

Yeah, the use of Rolle's theorem is that once you prove it, the rest of basic differential calculus just pops out.

"Rolle's Theorem: Practical Applications"

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