f'(x)=n(1+n^2x^2)-nx(2n^2x)/dominator squared

f'(x)=0

n(1+n^2x^2)-nx(2n^2x)=0

n+n^3x^2-2x^2n^3=0

n-n^3x^2=0

1-n^2x^2=0

x=+- sqrt(1/n)

f(1/n)=1/2 got it

so i see that we take the extreme points of the expression and do a limit on them

correct?(could you please help me with the question bellow about the cauchy serieses,you have been very helpfull)