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Question
Check the validity of the Rolle’s theorem for the following function:
f(x) = `x^(2/3), x ∈ [ - 1, 1]`
Solution
f(x) = `x^(2/3)`
∴ f'(x) = `d/dx(x^(2/3))`
= `(2)/(3)x^(-1/3)`
= `(2)/(3root(3)(x)`
This does not exist at x = 0 and 0 ∈ (– 1, 1)
∴ f is not differentiable on the interval (– 1, 1).
Hence, the conditions of Rolle's theorem are not satisfied.
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