Suppose that you are climbing a hill whose shape is given by z = 468 − 0.06 x2 −0.02 y2, and that you are at the point (50, 30, 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) ???

Question

Suppose that you are climbing a hill whose shape is given by z = 468 − 0.06 x2 −0.02 y2, and that you are at the point (50, 30, 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) ???