求导函数可得，f′（x）=3x2+6ax+3（a+2）∵函数f（x）=x3+3ax2+3（a+2）x+1既有极大值又有极小值，∴f′（x）=3x2+6ax+3（a+2）=0有两个不等的实数根∴△=36a2-36（a+2）＞0∴a2-a-2＞0∴a＜-1或a＞2故选D
