# Rolle's Theorem

1. Nov 11, 2005

### physics_ash82

Ok I think I can use Rolles theorem on F(x)=x^2+3x on the inteval [ 0,2]
because the derivative can be defined
so then I think I use the formula [f(b)-f(a)] / [b-a] to find f'(c), then set f'(c) = F'(x) and solve is this process right?:shy:

2. Nov 11, 2005

### AKG

What are you even trying to prove?

3. Nov 11, 2005

### Jameson

It seems you're using the mean value theorem, which is the one you listed. Rolle's theorem says that if f(a)=f(b) on some closed interval, then there must be some point c such that f'(c)=0.

4. Nov 12, 2005

### mathwonk

rolles theorem is a trivial consequence of the obvious (but deep) fact that a continuous function f which takes the same value twice must have a local extremum in between.

then rolle says if f is also differentiable, the derivative is zero there.

the MVT is then a further trivial consequence of rolle.

i.e. both rolle and MVT are trivial, but useful consequences of one deep result about continuity.

my point is that the emphasis on these two as big time theorems is quite misplaced.

even their statements take away something from the result, since just knowing the derivative is zero somewhere in between two points is decidedly weaker than knowing there is a local extremum.

for instance the statement of rolles theorem does not imply that between two critical points of a continuously differentiable function there must be a flex, but the stronger result does.

Last edited: Nov 12, 2005
5. Nov 14, 2005