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Find the range of f(x)=x/(1+x^2)...

Find the range of `f(x)=x/(1+x^2)`

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`f(x)=x/(1+x^2)`
maximum when `f'(x)=0`
`f'(x)=d/(dx){x/(1+x^2)}`
`=((1+x^2)x-x*(dx))/(1+x^2)^2`
`=(1-x^2)/(1+x^2)^2`
`f'(x)=0, when,1-x^2=,x=pm1`
`max{f(x)}=1/(1+1)=1/2`
`min{f(x)}=-1/(1+1)=-1/2`
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