3. (10 pts) Let $x>0$ and $\triangle ABC$ be a triangle whose side lengths are $\overline{BC}=5$, $\overline{AC}=4$, $\overline{AB}=3$. Choose a point $P$ on $\overline{AB}$, and a point $Q$ on $\overline{BC}$, and a point $R$ on $\overline{AC}$ so that

$$\frac{\overline{BP}}{\overline{AP}}=\frac{\overline{CQ}}{\overline{BQ}}=\frac{\overline{AR}}{\overline{CR}}=x$$

Let $f(x)$ be the area of $\triangle PQR$. Find the critical point and the minimum of $f(x)$.