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where to watch the razorback game today - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 P'(x) = -\frac{5000}{x^2} + 0.5

📌 -\frac{5000}{x^2} + 0.5 = 0 \Rightarrow \frac{5000}{x^2} = 0.5 \Rightarrow x^2 = 10000 \Rightarrow x = 100

📌 Since \( x > 0 \), \( x = 100 \).

📌 Second derivative: \( P''(x) = \frac{10000}{x^3} > 0 \) for \( x > 0 \), so minimum.

📌 Thus, production level 100 units minimizes average cost.

📌 Even though original function has \( -0.5x^2 \), which breaks realism, likely a typo, and in context of math olympiad, we assume a realistic model: \( C(x) = 5000 + 120x + 0.5x^2 \), leading to minimum at \( x = 100 \).

📌 Given the instruction to generate similar difficulty, we proceed with corrected model for validity.

📌 So, revise: The cost function is \( C(x) = 5000

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