I'm supposed to find the maximum slope of the curve $\displaystyle y = 8x^3 + 2x^2$

My work:

$\displaystyle y' = 24x^2 + 4x$

$\displaystyle y'' = 48x + 4$

$\displaystyle 24x^2 + 4x = 0$

$\displaystyle 4x(6x + 1) = 0$

$\displaystyle 6x + 1 = 0$

$\displaystyle x = \frac{-1}{6}$

My question is, am I supposed to solve for x in $\displaystyle y^{''}$ as well or no? Supposing I'm not but do I plug the value I got from x back into the original equation to solve for y then that gives me the maximum slope of the curve?