x>0. find the maximum value of x/(x^2 +1)?

2
1
0.2
0.5

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F'(x)=(x2+1)-x(2x)/(x2+1)2 F'(x)=0 for x2+1-2x2=-x2+1=0 So x=1 Put x=1 in the fUnction the value is 1/(1+1)=1/2=0.5