I'm having a little trouble with a problem that seems suspiciously easy and I wanted to make sure I'm on the right path. The problem reads as follows:
The rate of r (in liters per minute) at which water is entering a tank is given for t > 0 by the graph. A negative rate means that water is leaving the tank. In parts (a) – (d), give the largest interval on which: (a) The volume of water is increasing. (b) The volume of water is constant. (c) The volume of water is increasing fastest. (d) The volume of water is decreasing.
From my point of view it seems that the largest interval on which the function is increasing is also the largest interval on which it is increasing fastest. It also seems the largest intervals on which the function remains constant are the same length. Am I on the right track or am I misinterpreting the question?