Shares of a second stock minimising portfolio variance

You hold one share of stock $A$, whose return has mean $2$ and variance $4$. You will add $k$ shares of stock $B$, whose return per share has mean $3$ and variance $9$. The returns of $A$ and $B$ have correlation $-\tfrac12$. What value of $k$ makes the variance of the combined portfolio as small as possible?

$k=\tfrac13$. $\text{Cov}(A,B)=-\tfrac12\cdot2\cdot3=-3$, so the portfolio variance is $4+9k^2-6k$. Setting the derivative $18k-6$ to zero gives $k=\tfrac13$ (the means play no role).