Hi I'm studying foundation of analysis and working on mean value theorem

please give a statement and an example of each case.

1. Theorems on derivatives = o, at extreme point.
2. Theorems on increasing and decreasing at points when derivatives are not 0, including monotone functions
3. Theorems on f ' (prime) bounded on (a,b) => f is unif. cont. on (a,b)
4. Theorems on f ' (prime) exists on (a,b) => f ' (prime) satisfies the intermediate value theorem.

Thank you for your help.