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Home » \[ \frac\pi2 + \phi = \frac\pi2 + n\pi \quad \Rightarrow \quad \phi = n\pi \] - ToelettAPP

\[ \frac\pi2 + \phi = \frac\pi2 + n\pi \quad \Rightarrow \quad \phi = n\pi \] - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 To minimize \( P(x) \), take the derivative:

📌 P'(x) = -\frac{5000}{x^2} + 0 - 0.5 = -\frac{5000}{x^2} - 0.5

📌 Set \( P'(x) = 0 \):

📌 -\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

📌 This is always negative, meaning \( P(x) \) is decreasing? But that can’t be bounded. Recheck:

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