# How do you verify whether rolle's theorem can be applied to the function f(x)=absx in [-1,1]?

Nov 22, 2016

According to Rolle's Theorem, there are three criteria for us to able to apply the theorem:

1.) $f \left(x\right)$ must be continuous on $\left[a , b\right]$
2.) $f \left(x\right)$ must be differentiable on $\left(a , b\right)$
3.) $f \left(a\right) = f \left(b\right)$

#### Explanation:

$f \left(x\right) = | x | \to$ is not differentiable at x=0 which is$\in \left[- 1 , 1\right]$

$\therefore$ We cannot apply Rolle's Theorem