求y=(x-1)(x+3)^3的单调区间

2025-12-14 15:20:54
推荐回答(1个)
回答1:

y' = (x+3)^3 + (x-1)*3(x+3)^2 = (x+3)^2 [ x+3 + 3(x-1)] = 4x(x+3)^2,
x<-3时, y' < 0,
-3<=x<0时, y'<0,
00.
y=(x-1)(x+3)^3在x<0时单调递减, 在x>0时单调递增.