Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 50

The graph below shows how the temperature $T$ affects the maximum sustainable swimming
speed $S$ of Coho Salmon.



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



b.) Estimate the values $S'(15)$ and $S'(25)$ and interpret them.








$\quad$ a.) The meaning of the derivative of $S'(T)$ is the rate at which the speed of Coho Salmon
varies with respect to temperature; its unit is $\displaystyle \frac{cm}{s^2}$



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



$\qquad\displaystyle S'(15) \approx 0.375 \frac{cm}{s^2}$



$\qquad\displaystyle S'(25) \approx -0.4 \frac{cm}{s^2}$



$\quad$These values represents the acceleration of the salmon with respect to the temperature, the acceleration
of the salmon increases up to $20^\circ\rm{C}$. However, the acceleration starts to decrease beyond $20^\circ\rm{C}$