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Home » n = 12: 121+144+169=121+144=265+169=434 - go-checkin.com

n = 12: 121+144+169=121+144=265+169=434 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 ### Question 10

📌 The function \(f(x) = 3x^3 - 2x^2 + x - 5\) has a critical point at \(x = 1\). Determine if it is a maximum, minimum, or neither.

📌 First derivative: \(f'(x) = 9x^2 - 4x + 1\)

📌 \(f'(1) = 9(1)^2 - 4(1) + 1 = 6\) (not zero, so not a critical point, but let's check second derivative)

📌 Second derivative: \(f''(x) = 18x - 4\)

📌 \(f''(1) = 18(1) - 4 = 14\) (positive, indicating a local minimum if \(f'(1) = 0\))

📌 Since \(f'(1)

📌 eq 0\), \(x = 1\) is neither a maximum nor a minimum.

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