早教吧作业答案频道 -->数学-->
求函数f(x)=(x-4)*(x+1)^(2/3)的导数为0时x的值
题目详情
求函数f(x)=(x-4)*(x+1)^(2/3)的导数为0时x的值
▼优质解答
答案和解析
f(x)=(x+1-5)(x+1)^(2/3)
f(x)=(x+1)^(5/3) - 5(x+1)^(2/3)
f'(x)=5/3 (x+1)^(2/3) - 10/3 (x+1)^(-1/3)=0
(x+1)^(2/3)-2(x+1)^(-1/3)=0
(x+1)^(2/3)/(x+1)^(-1/3)=2
(x+1)^(2/3+1/3)=2
x+1=2
x=1
f(x)=(x+1)^(5/3) - 5(x+1)^(2/3)
f'(x)=5/3 (x+1)^(2/3) - 10/3 (x+1)^(-1/3)=0
(x+1)^(2/3)-2(x+1)^(-1/3)=0
(x+1)^(2/3)/(x+1)^(-1/3)=2
(x+1)^(2/3+1/3)=2
x+1=2
x=1
看了求函数f(x)=(x-4)*(...的网友还看了以下：