Question

If a function satisfy Rolle 's theorem,does it mean it FOR SURE satisfy mean value theorem as well?

Answer 1

What's Rolle's Theorem?
What's the Mean Value theorem?

Answer 2

[a.b] -> cts, (a,b) -> differentiable, then f'(c) exist in between that interval

Answer 3

and also what's the difference between them? because mean value theorem improves on rolle's theorem, so there should be a difference?

Answer 4

rolle's theorem can be sean as a special case of mean value theorem

Answer 5

The requirements for it to satisfy the mean value theorem are alsi necessary for it to satisfy rolles, so is it satisfy rolles, it satisfy the mean value as well

Answer 6

got it?

Answer 7

ok thanks.
So there difference betweene them is just f'(c)
in rolle, f'(c) = 0
in MVT, f'(c) = f(b)-f(a)/ b-a

Answer 8

right

Answer 9

yep, got it thanks both of u