Varify Lagrange's mean value theorem for the function
`f(x)=x+(1)/(x), x in [1, 3]`

Explanation

To verify Lagrange's Mean Value Theorem (LMVT) for the function \( f(x) = x + \frac{1}{x} \) on the interval \([1, 3]\), we will follow these steps:

### Step 1: Check the conditions of LMVT
Lagrange's Mean Value Theorem states that if a function \( f \) is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), then there exists at least one \( c \) in \((a, b)\) such that:

\[ f'(c) = \frac{f(b) - f(a)}{b - a} \]
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