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Home » C = \pi d = 10\pi - Aurero

C = \pi d = 10\pi - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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I'(t) = \frac{1000(t^2 + 10) - 1000t(2t)}{(t^2 + 10)^2} = \frac{1000t^...
Set \( I'(t) = 0 \):
-1000t^2 + 10000 = 0 \Rightarrow t^2 = 10 \Rightarrow t = \sqrt{10} \q...
To confirm it’s a maximum, check the sign of \( I'(t) \): decreasing b...
Thus, the infection rate peaks at \( t = \sqrt{10} \) days.
\(\boxed{\sqrt{10}}\)
Question:** A venture capitalist is evaluating a cleantech startup’s c...
The cost per unit is \( P(x) = \frac{C(x)}{x} = \frac{5000 + 120x - 0....
To minimize \( P(x) \), take the derivative:
P'(x) = -\frac{5000}{x^2} + 0 - 0.5 = -\frac{5000}{x^2} - 0.5

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