Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. a) What is the meaning of the derivative S’(T)? What are its units? b) Estimate the values of S’(10) and S’(18) and interpret them (Here you have to draw a tangent line on the point of the graph, t = 10 y t = 18 and calculate its slope) answers

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.

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