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Home » This is a Riemann sum. Split the sum: - AMAZONAWS

This is a Riemann sum. Split the sum: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Thus, the revenue growth rate is maximized at \( t = rac{5 - \sqrt{7}}{9} \).

📌 oxed{rac{5 - \sqrt{7}}{9}}

📌 A pharmacologist is studying the concentration of a new Alzheimer's drug in the bloodstream, modeled by the function \( C(x) = 5x^2e^{-x} \). Determine the dosage level \( x \) that maximizes the concentration.

📌 To find the dosage level that maximizes the concentration, we first find the derivative of \( C(x) \):

📌 C'(x) = rac{d}{dx}(5x^2e^{-x}).

📌 Using the product rule, where \( u = 5x^2 \) and \( v = e^{-x} \), we have:

📌 C'(x) = u'v + uv' = (10x)e^{-x} + 5x^2(-e^{-x}) = e^{-x}(10x - 5x^2).

📌 Set \( C'(x) = 0 \) to find critical points:

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