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Home » Therefore, the number of permutations satisfying both conditions is: - Tacotoon

Therefore, the number of permutations satisfying both conditions is: - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 I''(t) = rac{N'(t)D(t) - N(t)D'(t)}{[D(t)]^2}.

📌 Compute derivatives:

📌 N'(t) = 2 - 4t^3, \quad D'(t) = 2(1 + t^3)(3t^2) = 6t^2(1 + t^3).

📌 I''(t) = rac{(2 - 4t^3)(1 + t^3)^2 - (2t - t^4)(6t^2(1 + t^3))}{(1 + t^3)^4}.

📌 Factor \( (1 + t^3) \) from numerator:

📌 I''(t) = rac{(1 + t^3)\left[(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)

📌 ight]}{(1 + t^3)^4} = rac{(2 - 4t^3)(1 + t^3) - 6t^2(2t - t^4)}{(1 + t^3)^3}.

📌 First term:

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