Find the positive critical point of the function f(x)=x/(x^6+9)

Answer 1

f = x/(x^6+9)
f' = (9-5x^6)/(x^6+9)^2
f" = 6x^5(5x^6-53)/(x^6+9)^3
since the denominator is never zero, we just need to find where
6x^5(5x^6-53) = 0
That is at x=0, x = ±(53/6)^(1/6) = ±1.4377