3. Given the infinite sequence $\left\{a_{n}\right\}$, the sum of the first $n$ terms $S_{n}=-2 n^{3}+21 n^{2}+23 n$, then
A. $S_{n}$ has a minimum value, and the minimum value is 42
B. $S_{n}$ has a minimum value, and the minimum value is 46
C. $S_{n}$ has a maximum value, and the maximum value is 204
D. $S_{n}$ has a maximum value, and the maximum value is 504
3. D Hint: Let $f(x)=-2 x^{3}+21 x^{2}+23 x$, then $f^{\prime}(x)=-6 x^{2}+42 x+23, f^{\prime}(x)=0, x \approx 7$. Also, $f(7)=f(8)=504$. And $f^{\prime}(7)<0$.