Application Of Derivatives

Let $P(x)$ be a polynomial of degree 3 having extreme value at $x=1$. If $\mathop {\lim }\limits_{x \to 0}\left(\frac{P(x)+4}{x^2}+2\right)=6$, then $\left(\frac{d P}{d x}\right)_{x=\frac{1}{2}}=$