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The Derivative

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The Definition of the Derivative

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Power and Sum Rules

Suppose that, during a flu epidemic, the number of people ill with flu symptoms can be approximated by the function \[N(t)=90t^2-t^3, \quad 0\leq t \leq 70\] where \(t\) is measured in days since the beginning of the epidemic.

At what rate are flu symptoms spreading on day \(15\) of the epidemic, and how many people are ill with the flu on day \(15\)?

At what rate is the flu spreading on day \(65\)?

When is the flu spreading at the rate of \(1500\) people per day?