I am to determine the inflection point and intervals where the graph is concave up and concave down, and I have gotten a wrong answer somehow. I'm guessing it's probably when I solved for y'', it was a very long derivative to simplify:

$\displaystyle y = \frac{ln(x)}{6\sqrt{x}} $

$\displaystyle y' = \frac{6\sqrt(x)-ln(x)3\sqrt{x}}{36x^2} $

$\displaystyle y'' = \frac{3\sqrt(x)ln(x)-12\sqrt{x}}{36x^3} $

$\displaystyle y''=0 $ when $\displaystyle x=e^4 $