Section 14.5 Chain Rule

The length \(l\), width \(w\), and height \(h\) of a box change with time. At a certain instant the dimensions are \(l = 1\) m and \(w = h = 2\) m, and \(l\) and \(w\) are increasing at a rate of 2 m/s while \(h\) is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume (b) The surface area (c) The length of a diagonal