Let \(\mathrm{f}:[\mathrm{a}, \mathrm{b}] \rightarrow \mathbb{R}\) be such \(\mathrm{f}\) is differentiable in \((\mathrm{a}, \mathrm{b}), \mathrm{f}\) is continuous at \(\mathrm{x}=\mathrm{a} \& \mathrm{x}=\mathrm{b}\) and moreover \(\mathrm{f}(\mathrm{a})=0=\mathrm{f}(\mathrm{b}) .\) Then
(A) there exists at least one point \(c\) in \((a, b)\) such that \(f^{\prime}(c)=f(c)\)
(B) \(f^{\prime}(x)=f(x)\) does not hold at any poit in \((a, b)\)
(C) at every point of \((a, b), f^{\prime}(x)>f(x)\)
(D) at every point of \((a, b), f^{\prime}(x)<f(x)\)