Choose the correct alternative in the following:

$f(x)=\sqrt{x^{2}-10 x+25}$

$\Rightarrow f(x)=\sqrt{x^{2}-(2)(5) x+5^{2}}$

$\Rightarrow f(x)=\sqrt{(x-5)^{2}}$

$\Rightarrow f(x)=|x-5|$

$\Rightarrow f(x)=\left\{\begin{array}{c}(x-5), x-5 \geq 0 \Leftrightarrow x \geq 5 \\ -(x-5), x-5<0 \Leftrightarrow x<5\end{array}\right.$

$\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=\left\{\begin{array}{c}1, \mathrm{x} \geq 5 \\ -1, \mathrm{x}<5\end{array}\right.$

Since there is no fixed value of $f^{\prime}(x)$ in the interval $[0,7]$, so the answer is $(D)$ none of these