Let $D(A)$ be the derived $(\infty,1)$-category of some abelian category $A$. For which $A$ is $D(A)$ locally cartesian closed?

Replace $D$ with $D^b$ or similar if appropriate.

I essentially want to show that for any $f:x\to y$ in $D(A)$, the pullback functor $f^*: D(A)/y\to D(A)/x$ has a right adjoint $f_*$. However I am having trouble imagining what $f_*$ would look like in a derived category $D(A)$.