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Home » Chrome Nail Polish Hacks That Are Taking Social Media by Storm! - Sterling Industries

Chrome Nail Polish Hacks That Are Taking Social Media by Storm! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 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}

📌 Set \( I'(t) = 0 \):

📌 -1000t^2 + 10000 = 0 \Rightarrow t^2 = 10 \Rightarrow t = \sqrt{10} \quad (\text{since } t \geq 0 \text{ for time})

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