(a) What is the rate of change of $f(x,y) = 2xy+y^{2}$ at the point $(3,1)$ in the direction $\vec v = 2\boldsymbol{i}+3\boldsymbol{j}$?
$f_{\vec v} =$

(b) What is the direction of maximum rate of change of $f$ at $(3,1)$?
direction =
(Give your answer as a vector.)

(c) What is the maximum rate of change?
maximum rate of change =