If $f\;(x)$ is a two degree polynomial such that $f\;(3)=f\;(-3)$ and $a, b, c$ are in $AP$, then $f'(a)$, $f'(b)$ and $f'(c)$ are in

Question

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None\;of\;these$