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Home » To find the critical points, we compute the derivative \( g'(t) \) and set it to zero. - AMAZONAWS

To find the critical points, we compute the derivative \( g'(t) \) and set it to zero. - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 - 2t^3 - 4t^6 - 12t^3 + 6t^6 = 2 - 14t^3 + 2t^6.

📌 I''(t) = rac{2t^6 - 14t^3 + 2}{(1 + t^3)^3}.

📌 Set numerator of \( I''(t) = 0 \):

📌 2t^6 - 14t^3 + 2 = 0 \quad \Rightarrow \quad t^6 - 7t^3 + 1 = 0.

📌 Let \( u = t^3 \), then:

📌 u^2 - 7u + 1 = 0 \quad \Rightarrow \quad u = rac{7 \pm \sqrt{49 - 4}}{2} = rac{7 \pm \sqrt{45}}{2} = rac{7 \pm 3\sqrt{5}}{2}.

📌 Since \( t > 0 \), we take the positive root:

📌 t^3 = rac{7 + 3\sqrt{5}}{2} \quad \Rightarrow \quad t = \left( rac{7 + 3\sqrt{5}}{2}

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