Question

求助微积分~在线等！！

f(x)=x^2/(x-4)^2

1.垂直渐近线
2.水平渐近线
3.f(x)在哪个区间递增
4.f(x)在哪个区间递减
5.极大值
6.极小值
7.f(x)在哪个区间向下凹
8.f(x)在哪个区间向上凸

Answer 1

f(x)=x^2/(x-4)^2， f ' (x)= -(8 x)/(-4 + x)^3；f '' (x)=(16 (2 + x))/(-4 + x)^4
1.垂直渐近线： x=4
2.水平渐近线 y=1
3.f(x)在哪个区间递增 0 <= x < 4
4.f(x)在哪个区间递减 x <= 0 或 x > 4
5.极大值 无
6.极小值 y(0)=0
7.f(x)在哪个区间向下凹 -2 <= x < 4 或x > 4
8.f(x)在哪个区间向上凸 x <= -2

Answer 2