Question

What are the three conditions of Rolle’s theorem?

Answer 1

The three conditions of Rolle’s theorem are as follows:

If a function $f\left(x\right)$ is defined on a closed interval $\left[a,b\right]$ then it satisfies the following conditions:

• $f\left(x\right)$ is continuous on a closed interval $\left[a,b\right]$
• $f\left(x\right)$ is derivable on the open interval $\left(a,b\right)$
• $f\left(a\right)=f\left(b\right)$

Then there exists at least one value $c\in \left[a,b\right]$ such that $f\text{'}\left(c\right)=0$.