14. Find the minimum and maximum values of the function $y=\frac{x-2}{x^{2}-4 x+5}$ on $x \in\left[\frac{5}{2}, 3\right]$.
14. $y=\frac{(x-2)}{(x-2)^{2}+1}$, let $t=x-2$, then $t \in\left[\frac{1}{2}, 1\right], y=\frac{t}{t^{2}+1}=\frac{1}{t+\frac{1}{t}}$, since the function $g(t)=t+\frac{1}{t}$ is monotonically decreasing on $\left[\frac{1}{2}, 1\right]$, hence $y_{\max }=\frac{1}{1+1}=\frac{1}{2} ; y_{\min }=\frac{1}{\frac{1}{2}+2}=\frac{2}{5}$.