Question

函數(shù)y=x³-3x²-9x(-2＜x＜2)有(    )

A.極大值為5，極小值為-27              B.極大值為5，極小值為-11

C.極大值為5，無(wú)極小值                 D.極大值為-27，無(wú)極小值

Answer 1

解析：f′(x)=3x²-6x-9=3(x+1)(x-3),

令f′(x)=0得x₁=-1,x₂=3(舍去).

當(dāng)-2＜x＜-1時(shí)，f′(x)＞0;

當(dāng)-1＜x＜2時(shí)，f′(x)＜0.

∴當(dāng)x=-1時(shí)，f(x)有極大值，

f(x)_極大值=f(-1)=5,無(wú)極小值.

答案:C