Rolle's Theorem: Practical Applications

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

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving