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Home » The formula for the surface area \( A \) of a sphere is: - DNSFLEX

The formula for the surface area \( A \) of a sphere is: - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 P'(x) = -\frac{5000}{x^2} - 0.5 \quad \text{— still negative?}

📌 Wait — no, derivative of \( -0.5x \) is \( -0.5 \), derivative of \( 5000/x \) is \( -5000/x^2 \), so total:

📌 This is always negative, meaning cost per unit decreases as \( x \) increases? But the model \( C(x) = 5000 + 120x - 0.5x^2 \) is only positive for \( x < 250 \), and the current version increases linearly in cost, but quadratic loss? Actually, the cost function models *reducing* average cost? Let's reconsider.

📌 Wait — cost per unit: \( P(x) = \frac{5000}{x} + 120 - 0.5x \)

📌 But as \( x \to 0^+ \), \( 5000/x \to \infty \); as \( x \to \infty \), \( -0.5x \to -\infty \), but \( 5000/x \to 0 \), so \( P(x) \to -\infty \)? That's impossible.

📌 Likely a typo in interpretation. For realistic models, average cost typically has a minimum.

📌 But given: \( C(x) = 5000 + 120x - 0.5x^2 \). This implies fixed startup cost 5000, linear marginal cost 120, but reduced fixed cost at higher volume — unusual.

📌 But proceeding with given function.

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