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devil in the family the fall of ruby franke - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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}.

📌 To determine which critical point maximizes the growth rate, we evaluate the second derivative:

📌 R''(t) = rac{d}{dt}(9t^2 - 10t + 2) = 18t - 10.

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