Question

Does Rolle's theorem apply absolute value?

Answer 1

Rolle's theorem : Rolle’s theorem states that if a function $\text{'}f\text{'}$ is continuous on the closed interval $[a,b]$and

differentiable on the open interval $(a,b)$ such that $f\left(a\right)=f\left(b\right)$, then $f\prime \left(x\right)=0$for some $\text{'}x\text{'}$ with $a\le x\le b$.

Hence, the Rolle's theorem not applicable for absolute value.