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Home » Carnivine Secrets: Could This Superfood Revolution Your Diet Overnight? - Appfinity Technologies

Carnivine Secrets: Could This Superfood Revolution Your Diet Overnight? - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 P'(t) = -1000 \cdot \frac{-4.5e^{-0.5t}}{(1 + 9e^{-0.5t})^2} = \frac{4500e^{-0.5t}}{(1 + 9e^{-0.5t})^2}.

📌 To find the maximum of $ P'(t) $, we define:

📌 f(t) = \frac{e^{-0.5t}}{(1 + 9e^{-0.5t})^2}.

📌 Let $ u = e^{-0.5t} $, so $ f(t) = \frac{u}{(1 + 9u)^2} $. Now find the maximum of this function with respect to $ u > 0 $.

📌 f(u) = \frac{u}{(1 + 9u)^2}.

📌 Differentiate using the quotient rule:

📌 f'(u) = \frac{(1 + 9u)^2 \cdot 1 - u \cdot 2(1 + 9u)(9)}{(1 + 9u)^4}.

📌 Simplify numerator:

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Wait: maybe the remaining 190 is split into three equal parts → each 1...
But since question likely expects decimal or fraction, but format uses...
Alternatively: miscalculation?
Total: 720
Hours: 6 Heads per hour? No: plan is 720 in 6 hours → 120/hr.
After 2 hours: 240
Third hour: +50 more than second hour → but second hour: same rate → 1...
So third hour: 120 + 50 = 170.
Total after 3 hours: 240 + 170 = 410
Remaining: 720 - 410 = 310

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