It is certainly helpful to keep it in the form e(1/2)x2 and now I see that the max value of the fourth derivative is 43e2.
I am not sure why the first factor can be ignored, but for y = x4 + 6x2 + 3 I find a max value of 43 @ x=2.
So, which is it 43 or 43e2(317.729)?