If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2+cx,\; x \in [-1, 1]$, at the point $x= \frac{1}{2}$, then $2b+c$ equals :

Question

( A ) $1$
( B ) $-1$
( C ) $2$
( D ) $-3$