9. The maximum value of the function $f(x)=\sqrt{2 x-7}+\sqrt{12-x}+\sqrt{44-x}$ is
$f^{\prime}(x)=\frac{1}{\sqrt{2 x-7}}-\frac{1}{2 \sqrt{12-x}}-\frac{1}{2 \sqrt{44-x}}$ is monotonically decreasing in the interval $\left(\frac{7}{2}, 12\right)$, and $f^{\prime}(8)=\frac{1}{3}-\frac{1}{4}-\frac{1}{12}=0$, so $f(x)$ is monotonically increasing on $\left(\frac{7}{2}, 8\right)$ and monotonically decreasing on $(8,12)$, hence $f(x)_{\max }=f(8)=3+2+6=11$.