The concentration of salt in a fluid at $(x,y,z)$ is given by $F(x,y,z) = x^{2}+3y^{4}+x^{2}z^{2}$ mg/cm${}^3$. You are at the point $(1,1,1)$.

(a) In which direction should you move if you want the concentration to increase the fastest?
direction:
(Give your answer as a vector.)

(b) You start to move in the direction you found in part (a) at a speed of $3$ cm/sec. How fast is the concentration changing?
rate of change =