6. $f(x)=a x^{2}+(2 a-1) x-3$ has a maximum value of 1 on $\left[-\frac{3}{2}, 2\right]$, then the real number $a$ is
A. $-\frac{10}{3}$
B. $\frac{-3+2 \sqrt{2}}{2}$
C. $\frac{3}{4}$ or $\frac{-3+2 \sqrt{2}}{2}$
D. $\frac{3}{4}$ or $\frac{-3-2 \sqrt{2}}{2}$
6. D The maximum value of $f(x)$ can only be one of the following: $\frac{-12 a-(2 a-1)^{2}}{4 a}, f(2), f\left(-\frac{3}{2}\right)$. Discuss each case separately.