Verify Rolle's theorem for the function `f(x)=x^2+2x-8,``x in [-4,2]`.

Explanation

To verify Rolle's theorem for the function \( f(x) = x^2 + 2x - 8 \) on the interval \( [-4, 2] \), we need to check three conditions:

1. **Continuity on the closed interval \([-4, 2]\)**
2. **Differentiability on the open interval \((-4, 2)\)**
3. **Equality of function values at the endpoints: \( f(-4) = f(2) \)**

Let's go through each step in detail.

...