# What is the difference between rolle's theorem and mean value theorem?

##### 1 Answer

Jun 19, 2015

Rolle's Theorem is a special case of the Mean Value Theorem.

#### Explanation:

Difference 1 Rolle's theorem has 3 hypotheses (or a 3 part hypothesis), while the Mean Values Theorem has only 2.

Difference 2 The conclusions look different.

**BUT**

If the third hypothesis of Rolle's Theorem is true (**both** theorems tell us that there is a

The difference really is that the proofs are simplest if we prove Rolle's Theorem first, then use it to prove the Mean Value Theorem. After we have done that, we don't really need Rolle's Teorem for anything else. I mean, every **other** use (other than proving Mean Value) for Rolle's Theorem can be handled by the Mean Value Theorem.