Halliday, Resnick & Walker — Measurement: Problem 30

Water is poured into a container that has a small leak. The mass $m$ of the water is given as a function of time $t$ by $m = 5.00t^{0.8} - 3.00t + 20.00$, with $t \ge 0$, $m$ in grams, and $t$ in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) $t = 2.00\text{ s}$ and (d) $t = 5.00\text{ s}$?