Answer:
Here we have the relation between the speed of the salmon and the temperature.
a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )
[dS/dT ] = [m/s*°C ].
b) I can not do a draw of the figure, but i can give a aproximation.
For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.
then S'(18) ≈ 0 m/s*°C
this means that around this point the changes are small.
for T = 10°C
Around this region, we can see almost a linear behavior.
so we can take a range of +-2°C
S(12°C) = 25m/s
S(8°C) = 20m/s
then the slope can be obtained using the relation:
S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)
S = (25 - 20)/(12 - 8) = 5/4
then we have that S´(10°C) ≈ 5/4 m/s*°C
Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.
