The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. (b) Estimate the

Question

Eva8

6 days ago

12

The graph shows the influence of the temperature T on the maximum sustainable swimming speed S of Coho salmon. (b) Estimate the

values of S '(5) and S '(25).

Mathematics

2 answers:

zzz [4K] · Answer 1 · 2026-02-27T09:29:13+03:00

Based on the graph, it seems that S′(5) is approximately 2, while S′(25) seems to be around -2. The key observation is that these values are of opposite signs. This indicates that at roughly 5ºC, the Coho salmon experiences an increase of about 2 cm/sec in its maximum sustainable speed, whereas at 25ºC it encounters a decrease of approximately 2 cm/sec.

Svet_ta [4.3K] · Answer 2 · 2026-02-27T09:29:59+03:00

Answer:

To gain insights about S' (the derivative of S) from the graph of S:

For S'(5), we examine the curve's onset, where S(5) appears to be near 15 cm/s and shows an upward trend subsequently, indicating that S'(5) must be a positive value—meaning the swimming speed increases as temperature rises around T = 5°C.

Conversely, for S'(25), the graph indicates a decline after this temperature, suggesting that S'(25) is negative—implying that increasing the temperature beyond 25°C will lead to reduced speed.

We can estimate these values:

The average change rate in a segment can be expressed as:

S' = (Y2 - Y1)/(X2 - X1)

S is nearly linear between T = 5°C and 10°C where:

S(5) = 15 cm/s and S(10) = 20 cm/s

Thus, the average rate of change in this segment calculates to:

S' = (20 cm/s - 15 cm/s)/(10°C - 5°C) = 1 (cm/s°C)

Consequently, we can reasonably estimate S'(5) to be around 1 (cm/s°C).

A similar approach can be applied for S'(25):

We can assume S(20) = 25 cm/s and S(25) = 20 cm/s.

The average rate of change then becomes:

S' = (20 cm/s - 25 cm/s)/(25°C - 20°C) = -1 (cm/s°C)