(1 point) The concentration of salt in a fluid at (x, y, z) is given by F (x, y, z) = 2x2 + 3y4 + 236222 mg/cm3. 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 8 cm/sec. How fast is the concentration changing? rate of change = (1 point) Suppose that you are climbing a hill whose shape is given by z = 1443 0.07x2 0.08y2 , and that you are at the point (70, 100, 300). In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest? ( . ) If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)? (1 point) Find equations of the tangent plane and normal line to the surface 2 + 20 = xey cos z at the point (20, 0, 0). Tangent Plane: (make the coefficient of 2 equal to 1). = 0. Normal line: (20, , ) +t