12TH•Mathematics•Further Differentiation•Question 5
Solution
A team of environmental scientists is monitoring the oxygen level in a lake over time to ensure the water quality remains suitable for aquatic life. The oxygen level in the lake, measured in milligrams per liter (mg/L), is modeled by the equation: $O(t) = t^3 - 18t^2 + 81t + 100$ Where $O(t)$ is the oxygen level at time $t$ (in days after monitoring began). Scientists want to determine when during the monitoring period the oxygen level is at its lowest, as low oxygen levels can be harmful to fish and other aquatic organisms. Find the time $t$ when the oxygen level is at its minimum.
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