The length l, width w, and height h of a rectangular box (with a lid) change with time. At a certain instant the dimensions are l= 9 m, w= 4 m, h= 8 m, and l and w are increasing at a rate of 6 m/s...

The length l, width w, and height h of a rectangular box (with a lid) change with time. At a certain instant the dimensions are l= 9 m, w= 4 m, h= 8 m, and l and w are
increasing
at a rate of 6 m/s while h is
decreasing
at a rate of 9 m/s.

Suppose S the surface area of the box. At the given instant, we have: