Find the two stationary points of y=(3x^2+4)/x and determine if they are a local maximum, local minimum or neither.

I've made an attempt at the question and was wondering if someone could please check my answer and guide me if I've done something wrong

y = (3x^2+4)/x

= 3x+(4/x)

=3x+4x^-1

y' = 3-4x^2

0=3-4x^2

x = (-sqrt(3)/2) and (sqrt(3)/2)

Subbing the x into the original equation, y = -25/2sqrt(3) and 25/2sqrt(3)

I got that (-sqrt(3)/2,-25/2sqrt(3)) is a local minimum

and (sqrt(3)/2, 25/2sqrt(3)) is a local maximum.

Am I correct?