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Home » Differentiate with respect to time \( t \): - Feedz API

Differentiate with respect to time \( t \): - Feedz API

📅 May 16, 2026 👤 scraface

May 16, 2026

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\( x = 0 \):
C''(0) = e^0(5(0)^2 - 20(0) + 10) = 10 > 0 \quad ( ext{local minimum})...
C''(2) = e^{-2}(5(2)^2 - 20(2) + 10) = e^{-2}(20 - 40 + 10) = e^{-2}(-...
Therefore, the concentration is maximized at \( x = 2 \).
A historian of science is examining the impact of a scientific discove...
To find when the impact rate is increasing most rapidly, we need the m...
First, compute \( I'(t) \) using the quotient rule, where \( u = t^2 \...
I'(t) = rac{u'v - uv'}{v^2} = rac{(2t)(1 + t^3) - t^2(3t^2)}{(1 + t^...
I'(t) = rac{2t + 2t^4 - 3t^4}{(1 + t^3)^2} = rac{2t - t^4}{(1 + t^3)...
Now, find \( I''(t) \) to locate where \( I'(t) \) has a maximum:

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