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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 An angel investor is evaluating the growth potential of a tech startup. The companyâs revenue \( R(t) \) over time \( t \) (in years) is modeled by the function \( R(t) = 3t^3 - 5t^2 + 2t + 10 \). Determine the time \( t \) when the revenue growth rate is maximized.

📌 To find the time when the revenue growth rate is maximized, we first determine the derivative of the revenue function \( R(t) \) to find the growth rate:

📌 R'(t) = rac{d}{dt}(3t^3 - 5t^2 + 2t + 10) = 9t^2 - 10t + 2.

📌 Next, we find the critical points by setting \( R'(t) = 0 \):

📌 9t^2 - 10t + 2 = 0.

📌 Using the quadratic formula \( t = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 9 \), \( b = -10 \), and \( c = 2 \), we calculate:

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