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Home » As \( N o \infty \), \( rac1N+2 o 0 \), so: - Veritas Home Health

As \( N o \infty \), \( rac1N+2 o 0 \), so: - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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.

📌 To minimize \( P(x) = \frac{5000}{x} + 120 - 0.5x \), take derivative:

📌 Set to zero:

📌 No solution in reals — derivative never zero.

📌 But this suggests no critical point. However, for minimum, consider behavior.

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