1. The function $f(x)=-9 x^{2}-6 a x+2 a-a^{2}$ has a maximum value of -3 on the interval $\left[-\frac{1}{3}, \frac{1}{3}\right]$, then the value of $a$ can be
A. $-\frac{3}{2}$
B. $\sqrt{2}$
C. $\sqrt{6}+2$
D. $\sqrt{6}-2$
1. C $f(x)=-(3 x+a)^{2}+2 a, 3 x \in[-1,1]$. If $a \in[-1,1]$, then when $3 x=-a$, $[f(x)]_{\text {max }}=2 a=$ $-3, a=-\frac{3}{2}$, which is discarded; if $a>1$, then $3 x=-1,[f(x)]_{\text {max }}=-(-1+a)^{2}+2 a=-3, a=2 \pm \sqrt{6}$, where $2-\sqrt{6}$ is discarded.