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Home » Why These 5 Characters from Atlantis the Lost Empire Are Addictingly Relatable! - Baxtercollege

Why These 5 Characters from Atlantis the Lost Empire Are Addictingly Relatable! - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 C''(x) = e^{-x}(-10x + 5x^2 + 10 - 10x) = e^{-x}(5x^2 - 20x + 10).

📌 Evaluate \( C''(x) \) at the critical points:

📌 \( x = 0 \):

📌 C''(0) = e^0(5(0)^2 - 20(0) + 10) = 10 > 0 \quad ( ext{local minimum}).

📌 C''(2) = e^{-2}(5(2)^2 - 20(2) + 10) = e^{-2}(20 - 40 + 10) = e^{-2}(-10) < 0 \quad ( ext{local maximum}).

📌 Therefore, the concentration is maximized at \( x = 2 \).

📌 A historian of science is examining the impact of a scientific discovery over time, modeled by \( I(t) = rac{t^2}{1 + t^3} \), where \( t \) is time in centuries. Find the time \( t \) when the impact rate is increasing most rapidly.

📌 To find when the impact rate is increasing most rapidly, we need the maximum of the derivative of \( I(t) \):

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