When you come across accumulation of change questions, it is important to read each question carefully as one word may change the answer.
For example, part a is looking for how much water flows into the pipe during the interval.
In this case you would only use the function R(t) since the question is only asking for the amount of water flowing INTO the pipe.
In part D we are asked at what time will the pipe overflow. In this case you would need to include both R(t) [what is going in ] and D(t) [what is going out]
Note you also must include the initial amount (when time is equal to zero) since it is accounting for the total amount of water within the tank.
When determining a maximum or minimum like in part C, you must also use both equations since it is asking when the total amount of water is at a minimum. You would set R(t) - G(t) = 0 and solve for t. These are your critical points and you can use them in a table to determine a max or min.
Using the critical points and endpoints, plug each x value into the original function [R(t)-G(t) and get each y value. The highest Y value is the maximum, the lowest is the minimum!
Do not forget to inclue the endpoints in your table as the amount of water in the pipe could be at a max or min at either of those points!
Reading each question carefully and picking out trigger words is vital to these problems! If you only include one piece when both the in and out functions are required, your answer will be very far off!