Question

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals

`f(x) = |1/x|, x ∈ [- 1, 1]`

Answer 1

f(–1) = 1

f(1) = 1

⇒ f(–1) = f(1) = 1

But f(x) is not differentiable at x = 0

∴ Rolle’s theorem is not applicable.