JEE Math Practice Question

If the function $f(x)=2 x^3-9 a x^2+12 \mathrm{a}^2 x+1$, where $\mathrm{a}>0$, attains its local maximum and local minimum values at p and q , respectively, such that $\mathrm{p}^2=\mathrm{q}$, then $f(3)$ is equal to :

1. A.55
2. B.37
3. C.10
4. D.23