6. Given the function $f(x)=4 x^{3}-3 x$ has a maximum value in the interval $(a, a+2)$. Then the range of the real number $a$ is ( ).
(A) $\left(-\frac{5}{2},-1\right)$
(B) $\left(-\frac{5}{2},-1\right]$
(C) $\left(-\frac{5}{2},-\frac{1}{2}\right)$
(D) $\left(-\frac{5}{2},-\frac{1}{2}\right]$
6. B.

Notice that the only maximum point of $f(x)=4 x^{3}-3 x$ is $x=-\frac{1}{2}$, and $f\left(-\frac{1}{2}\right)=1=f(1)$.
$$
\begin{array}{l}
\text { Hence } a<-\frac{1}{2}<a+2 \leqslant 1 \\
\Rightarrow-\frac{5}{2}<a \leqslant-1 .
\end{array}
$$