Question

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

Answer 1

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

1.) `f(x)` must be continuous on `[a,b]`
2.) `f(x)` must be differentiable on `(a,b)`
3.) `f(a) = f(b)`

Explanation:

`f(x) = |x| ->` is not differentiable at x=0 which is`in[-1, 1]`

`:.` We cannot apply Rolle's Theorem