`"Verify LMVT for " f(x) =-x^(2)+4x-5 " and " x in [-1,1]`

Explanation

To verify the Lagrange Mean Value Theorem (LMVT) for the function \( f(x) = -x^2 + 4x - 5 \) on the interval \( [-1, 1] \), we will follow these steps:

### Step 1: Check Continuity
The first condition of LMVT states that the function must be continuous on the closed interval \([-1, 1]\).

**Solution:**
Since \( f(x) \) is a polynomial function, it is continuous everywhere, including the interval \([-1, 1]\).

...