12.11 $f(x)=\frac{(x-2)^{2}}{x^{2}}$.
12.11 The domain of the function is the entire number line, except for the point $x=0$. Using formula (12.4) and the table of derivatives, we find

$$
f^{\prime}(x)=\frac{2(x-2) x^{2}-(x-2)^{2} 2 x}{x^{4}}=\frac{4(x-2)}{x^{3}}
$$

$f^{\prime}(x)=0$ only at $x=2$. We will construct a table:

| Interval | $(-\infty, 0)$ | $(0,2)$ | 2 | $(2, \infty)$ |
| :---: | :---: | :---: | :---: | :---: |
| $f^{\prime}(x)$ | + | - | 0 | + |
| $f(x)$ | $\nearrow$ | $\searrow$ | $\min$ | $\nearrow$ |

Therefore, $x=2$ is a point of minimum; the function is increasing on $(-\infty, 0)$ and on $(2, \infty)$, and decreasing on $(0,2)$.