Question

函数f(x)=x/x²+6的单调性？

Answer 1

函数f(x)=x/(x^2+6)的单调性
f(x)=x/(x^2+6)
两边求导
f'(x)
=(x^2+6-2x^2)/(x^2+6)^2
=(-x^2+6)/(x^2+6)^2
f'(x)=0
x=√6 or -√6
f'(√6+)<0 , f'(√6-)>0
x=√6 (max)
f'(-√6+)>0 , f'(-√6-)<0
x=-√6 (min)
函数f(x)=x/(x^2+6)的单调性
递增 =[-√6, √6]
递减=(-∞, -√6] U [√6, +∞)

Answer 2

f(x) = x/(x²+6)
f'(x) = (x²+6-2x^2)/(x²+6) = (6-x^2)/(x²+6) , 驻点 x = ±√6
函数单调减少区间 x∈(-∞, -√6)∪(√6, +∞)
函数单调增加区间 x∈( -√6, √6)