`f(x) = (4x)/(x^2 + 1)` Find the critical numbers of the function.

Given `f(x)=(4x)/(x^2+1)`

Find the derivative using the Quotient Rule. The set the derivative equal to zero and solve for the critical x value(s).

`f'(x)=[(x^2+1)(4)-(4x)(2x)]/(x^2+1)=0`

`f'(x)=4x^2+4-8x^2=0`

`f'(x)=-4x^2+4=0`

`f('x)=-4(x^2-1)=0`

`x=1,x=-1`