Finding local minimum, local maximum or neither

So I'm trying to find the local minimum, maximum or neither for the following function:

f(x)=(x-1)^2 * (x+3)^2

I've already found the stationary points (1,0), (-1,16), (-3,0)

So do I plug the x values into the second derivative which is 12x^2 + 24x - 4

so for example (12*1)^2 + (24*1) - 4 = 164 which means it is local minimum

(12*-1)^2 + (24*-1) - 4 = 116 which means a local minimum

and (12*-3)^2 + (24*-3) - 4 = 1,220 which is also a local minimum...

I feel this is wrong though. Can someone give me some guidance?