MHB Derivatives and relative max's and min's

[kendalgenevieve]

f(x)=x^3-12x^2+15x+16
Use the first derivative to find relative maximums, minimums, or neither.

I am trying to find x to plug it back into f(x) to get my y value, but I am not sure if I am getting the correct x value. I did the first derivative and got 3x^2-24x+15. I then set it equal to 0 and got x=4+- the square root of 44.
Is this correct or am I getting the wrong x-value?

 

[MarkFL]

You have correctly computed $f'$, however the roots of $f'$ are not quite correct. These roots are in fact:

$$x=4\pm\sqrt{11}$$