Finding local minimum values

I am given the function ln(x^4 + 27) I took the derivative I got (4x^3)/(x^4+27) I found the critical number which was 0. I made intervals of (-infinity,0) and (0,infinity)

I found that the function was increasing on (0,infinty) and decreasing on (-infinty, 0) I found no local maxiumums. However I thought there would be a local minimum at x=0 but I'm wrong what is the local miniumum?

Re: Finding local minimum values

the function has no maximum, but an absolute minimum of $\displaystyle y = \ln(27)$ at $\displaystyle x = 0$ ... an absolute minimum is also a local minimum.