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Home » n^2 + (n+1)^2 = 85 - Groen Casting

n^2 + (n+1)^2 = 85 - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Solution: To find the local extrema of the function $ P(t) = t^3 - 6t^...
P'(t) = 3t^2 - 12t + 9.
Set $ P'(t) = 0 $ to find critical points:
3t^2 - 12t + 9 = 0 \Rightarrow t^2 - 4t + 3 = 0.
Factoring gives:
To determine the nature of these critical points, we use the second de...
P''(t) = 6t - 12.
Evaluate at the critical points:
P''(1) = 6(1) - 12 = -6 < 0 \Rightarrow \text{local maximum at } t = 1...
P''(3) = 6(3) - 12 = 6 > 0 \Rightarrow \text{local minimum at } t = 3.

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