Verify Lagrange's Mean value theorem for the function f(x) = `x^(2) -1` in the interval [3,5].

Explanation

To verify Lagrange's Mean Value Theorem (LMVT) for the function \( f(x) = x^2 - 1 \) on the interval \([3, 5]\), 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 \([a, b]\).

- The function \( f(x) = x^2 - 1 \) is a polynomial function.
- Polynomial functions are continuous everywhere.

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