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Home » Substitute \( p = 2 \), \( q = 2 \) into (1): - Blask

Substitute \( p = 2 \), \( q = 2 \) into (1): - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Thus, the minimum temperature is 8 degrees Celsius at 2 AM.

📌 Question:** An epidemiologist is analyzing the spread of a virus and models the number of infected individuals \( I(t) \) at time \( t \) days with the function \( I(t) = \frac{1000t}{t^2 + 10} \). Find the time \( t \) when the infection rate peaks.

📌 To find the time \( t \) when the infection rate peaks, we need to find the critical points of \( I(t) = \frac{1000t}{t^2 + 10} \) by taking the derivative and setting it to zero.

📌 First, apply the quotient rule for derivatives:

📌 If \( I(t) = \frac{u}{v} \), then \( I'(t) = \frac{u'v - uv'}{v^2} \).

📌 Let \( u = 1000t \), so \( u' = 1000 \);

📌 \( v = t^2 + 10 \), so \( v' = 2t \).

📌 I'(t) = \frac{1000(t^2 + 10) - 1000t(2t)}{(t^2 + 10)^2} = \frac{1000t^2 + 10000 - 2000t^2}{(t^2 + 10)^2} = \frac{-1000t^2 + 10000}{(t^2 + 10)^2}

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