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Home » Substituting gives \( x^2 + 2x - 15 = 0 \). - Richter Guitar

Substituting gives \( x^2 + 2x - 15 = 0 \). - Richter Guitar

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 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:

📌 t = rac{10 \pm \sqrt{(-10)^2 - 4 \cdot 9 \cdot 2}}{2 \cdot 9} = rac{10 \pm \sqrt{100 - 72}}{18} = rac{10 \pm \sqrt{28}}{18}.

📌 Simplifying further:

📌 t = rac{10 \pm 2\sqrt{7}}{18} = rac{5 \pm \sqrt{7}}{9}.

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