The number of salmon swimming upstream to spawn is approximated by S(x) = −x³ + 3x² + 360x + 5000, 6 ≤ x ≤ 20, where x represents the temperature of the water in degrees Celsius. Find the water temperature that produces the absolute maximum number of salmon swimming upstream.
Added by Gabriel L.
Step 1
S'(x) = -3x^2 + 6x + 360 Now, set S'(x) = 0 and solve for x: 0 = -3x^2 + 6x + 360 Show more…
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Adi S.
With $x$ representing the the water temperature in degrees Celsius and $2 le x le 30$. Then the function $S(x) = -x^3 + 48x^2 - 580x + 2000$ is an approximation to the number of salmon swimming upstream to spawn. Find the temperature that produces the maximum number of salmon and the temperature that produces the minimum number of salmon. SHOW ALL WORK and ALL key steps with the correct testing. Give your answer as a statement with units. ( 8 points)
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