Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 49

The quantity of oxygen that can dissolve in water depends on the temperature of the water.
The graph below shows how oxygen solubility $S$ varies as a function of the water temperature $T$.



a.) State what is the meaning of the derivative $S'(T)$ and its corresponding units.



b.) Estimate the value of $S'(16)$ and interpret it.






$\quad$ a.) The meaning of the derivative of $S'(T)$ is the rate at which the oxygen solubility changes with respect to the water
temperature; its unit is $\displaystyle \frac{\left(\frac{mg}{L}\right)}{^\circ\rm{C}}$



$\quad$ b.) Based from the graph,


$\qquad \displaystyle S'(16) \approx -0.2 \frac{\frac{mg}{L}}{^\circ\rm{C}}$


$\quad$ This value represents the rate of decrease of the oxygen content of water as the temperature increases.