Discuss the applicability of Rolles theorem for the function `f(x)=x^(2//3)` on `[-1,\ 1]`

Explanation

To determine the applicability of Rolle's theorem for the function \( f(x) = x^{2/3} \) on the interval \([-1, 1]\), we need to check the three conditions required by the theorem:

### Step 1: Check Continuity
Rolle's theorem requires that the function be continuous on the closed interval \([-1, 1]\).

1. **Function Definition**: The function \( f(x) = x^{2/3} \) is defined for all real numbers.
2. **Continuity**: Since \( x^{2/3} \) is a composition of continuous functions (the power function is continuous for all real numbers), \( f(x) \) is continuous on \([-1, 1]\).

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