Verify Rolle's theorem for the function f(x) = `x^(3) + 3x^(2) - 24x -80` in the interval `[-4,5]`.

Explanation

To verify Rolle's theorem for the function \( f(x) = x^3 + 3x^2 - 24x - 80 \) in the interval \([-4, 5]\), we will follow these steps:

### Step 1: Check the continuity of \( f(x) \)
Since \( f(x) \) is a polynomial function, it is continuous on the entire real line, including the closed interval \([-4, 5]\).

### Step 2: Check the differentiability of \( f(x) \)
Polynomial functions are also differentiable everywhere on the real line. Therefore, \( f(x) \) is differentiable on the open interval \((-4, 5)\).

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