This is always negative, meaning \( P(x) \) is decreasing? But that can’t be bounded. Recheck:
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- -\frac{5000}{x^2} - 0.5 = 0 \Rightarrow \frac{5000}{x^2} = -0.5
- This yields a negative right-hand side, which is impossible. But note: we made an error in sign — the derivative is:
- P'(x) = -\frac{5000}{x^2} - 0.5
- Actually,
- P(x) = \frac{5000}{x} + 120 - 0.5x
- P'(x) = -\frac{5000}{x^2} - 0.5 \quad \text{— still negative?}
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