7.1、确定函数的单调区间 y=2x^3-6x^2-18x-7

2025-06-28 13:17:18
推荐回答(2个)
回答1:

y' = 6X^2 - 12X - 18
令y' = 0
(X + 1)(X - 3) = 0
X = -1 或 X = 3
当X>=3 或 X <= -1 时,y' >= 0
当 -1 <= X <=3 时,y'<0
所以 X <= -1 时,递增
-1 <= X <=3 时,递减
X >=3 时,递增

回答2:

解:y'=6x^2-12x-18=6(x+1)(x-3);
令y'>0,则x<-1或x>3;令y'<0,则-1 所以y在区间(-∞,-1)和(3,+∞)上单调递增;在区间(-1,3)上单调递减。