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Home » How Allen the Alien Proves We’re Not Alone—Shocking Evidence Inside! - Abbey Badges

How Allen the Alien Proves We’re Not Alone—Shocking Evidence Inside! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 10x - 5x^2 = 0 \quad \Rightarrow \quad 5x(2 - x) = 0.

📌 Thus, \( x = 0 \) or \( x = 2 \).

📌 To determine which value maximizes \( C(x) \), evaluate the second derivative:

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

📌 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}).

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