Question

确定f(x)=(x-1)(x+1）^3的单调区间

Answer 1

f(x)=(x-1)(x+1)³
f'(x)=(x+1)³+(x-1)*3(x+1)²=0
∴x=1/2或-1
当x<-1时，f'(x)<0 f(x)单调递减
当-1≤x<1/2时，f'(x)<0 f(x)单调递减
当x≥1/2时，f'(x)>0 f(x)单调递增
∴单调递增区间[1/2,+∞)，单调递减区间(-∞,1/2)
希望对你有帮助~

Answer 2

f(x)=(x-1)(x+1）^3
f'(x)=(x+1）^3+3(x-1)(x+1）^2=(x+1）^2(4x-2)
当x＞1/2,f'(x)＞0
当x＜1/2,f'(x)≤0
所以当x＞1/2，f(x)单调增，当x＜1/2，f(x)单调减