Verify Rolle's theorem for the function ` f(x) = x^(3) - 9x^(2) + 26x -24` in the interval [2.4]

Explanation

To verify Rolle's theorem for the function \( f(x) = x^3 - 9x^2 + 26x - 24 \) in the interval \([2, 4]\), we will follow these steps:

### Step 1: Check the conditions of Rolle's Theorem

Rolle's theorem states that if a function \( f(x) \) is continuous on the closed interval \([a, b]\), differentiable on the open interval \((a, b)\), and \( f(a) = f(b) \), then there exists at least one \( c \) in the interval \((a, b)\) such that \( f'(c) = 0 \).

### Step 2: Verify continuity and differentiability

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