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v/h/s/2 - Sourci

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Since \(x > 4\), \(x = 2 + 2\sqrt{3} \approx 5.464\).

📌 #### #### 5.464

📌 The function \( f(x) = x^3 - 6x^2 + 9x + c \) has a local maximum at \( x = 1 \). Find \( c \) if \( f(1) = 2 \).

📌 Solution 8:

📌 \( f'(x) = 3x^2 - 12x + 9 \).

📌 Setting \( f'(x) = 0 \) for critical points:

📌 3x^2 - 12x + 9 = 0 \Rightarrow x^2 - 4x + 3 = 0 \Rightarrow (x-3)(x-1) = 0

📌 So \( x = 1 \) and \( x = 3 \) are critical points.

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