fee2998f0bf25e4d24dbedcea88080b8.gif

Here I have graphed y and y'

y'=0 where x=4.139 (to 3decimal places)

so there is a local minimum at x=4.139

If the domain was restricted to $\displaystyle (0,\infty]$ (I think that is how you write it, please correct me if i am wrong)

then this would be the minimum.