求曲线y=(x-1)乘以³√X²的凹凸区间及拐点
问题描述:
求曲线y=(x-1)乘以³√X²的凹凸区间及拐点
答
先求导
y‘=³√X² +(2/3)×(x-1)×x^(-1/3)
再求导y''=(2/3)x^(-1/3) +(2/3)x^(-1/3)-2/9(x-1)x^(-4/3)>0解得x>-0.2
当y''=(2/3)x^(-1/3) +(2/3)x^(-1/3)-2/9(x-1)x^(-4/3)<0解得x<-0.2
故曲线的拐点是在x=0.2时取得曲线的凹区间是(-0.2,+∞) 凸区间是(-∞,-0.2)