3. (10 points) Given

$$f(t)= \begin{cases} 1, & t\le 0 \\ 1-t, & t>0 \end{cases}$$

and

$$F(x)=\int_{-1}^{2ax+2} f(t)\,dt$$

with $a>0$, find $a$ so that $F$ is maximum at $x=-2a$.