The concentration of salt in a fluid at the point (x,y,z) is given by S(x,y,z) = x2 + y4 + x2z2 (in mg per cubic cm). You are at the point (1, 1, 1)....

The concentration of salt in a fluid at the point (x,y,z) is given by S(x,y,z) = x2 + y4 + x2z2 (in mg per cubic cm). You are at the point (−1, 1, 1).

(a) In which direction should you move if you want the concentration to increase the fastest?

(b) You start to move in the direction you found in part (a) at a speed of 4 cm/sec. How fast is the concentration (of salt) changing?