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DM
Numerade Educator

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Problem 58 Hard Difficulty

The graph 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'(15) $ and $ S'(25) $ and interpret them.

Answer

a) The units of $S^{\prime}(T)$ are centimeters per second per Celsius. $\\$
b) 0.71 $\frac{cm}{s\cdot \degree C} $ ; 1.6 $\frac{cm}{s\cdot \degree C} $

Discussion

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CA

Catherine A.

October 23, 2020

Calculus: Early Transcendentalshas kept me up at night until I found this

DG

David Base G.

October 23, 2020

Daniel, thanks this was super helpful.

Video Transcript

and this problem, we're given this graph looks like this for the maximum sustainable swimming speed s of coho salmon. And the first question we were asked is what is the meaning of the derivative S. Prime at T. It's probably pretty well this is the rate of change, so do so that ready to change of the maximum sustainable. Okay, speed. Uh Coho salmon with respect two. Oh, temperature. Yeah. Okay. The next part were asked to estimate the values of S prime at five and S prime at 25. Okay. Right, so we can tell that the tangent line at five right, looks like that. It passes through the points 5, 10 and 10.20 Or 5 15. Excuse Me? 5, 15 and 10, 20. Okay, So using those points we can have 20 minus 15 Over 10 -5. Using our two points, so that gives us 5/5, which is one and this is in centimeters per second degrees C. Okay, so then at 25 At T. equals 25. Yeah. Yeah. So Yeah. Yeah, well, depending on how we look at it, okay, If this were s prime at 20, yeah, then what we would be like at the maximum. So this would be a zero slope at 25. Okay, We're falling again and it looks like it's about the opposite negative of S at five. So this Would be -1cm for a second degree C. So there you go. One change. Okay,