Question

函数f(x)=x/1+x²是定义在R上的奇函数,且f(1/2)=2/5.求:f(x)的单调减区间并判断f(x)

Answer 1

f(x)=x/(1+x^2)

f'(x)=(1+x^2-x(2x))/(1+x^2)^2

=(1-x^2)/(1+x^2)^2

f'(x)>0

(1-x^2)/(1+x^2)^2>0

1-x^2>0

x^2-1