Let \(f(x)=\frac{1}{x^{2}}\) and \(g(x)=\frac{1}{x}\), for all x ∈ [a, b] with 0 < a < b. Then by Cauchy's mean value theorem, there exists c ∈(a, b) such that \(\frac{f^{\prime}(c)}{g^{\prime}(c)}=\frac{f(b)-f(a)}{g(b)-g(a)}\), where c is