Verify Lagrange's mean theorem for the function `f(x) =x^(2) + x-1 ` in the interval [0,4]

Explanation

To verify Lagrange's Mean Value Theorem (LMVT) for the function \( f(x) = x^2 + x - 1 \) on the interval \([0, 4]\), we will follow these steps:

### Step 1: Check continuity and differentiability
The function \( f(x) = x^2 + x - 1 \) is a polynomial function. Polynomial functions are continuous and differentiable everywhere on the real line.

### Step 2: Calculate \( f(a) \) and \( f(b) \)
Let \( a = 0 \) and \( b = 4 \).
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