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Home » \( 4 = \frac21 - r \). - Groen Casting

\( 4 = \frac21 - r \). - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 First, find the derivative: \( f'(x) = 3x^2 - 6x \).

📌 Set \( f'(x) = 0 \) to find critical points: \( 3x(x - 2) = 0 \).

📌 So, \( x = 0 \) or \( x = 2 \).

📌 Use the second derivative test: \( f''(x) = 6x - 6 \).

📌 At \( x = 0 \), \( f''(0) = -6 \) (local maximum).

📌 At \( x = 2 \), \( f''(2) = 6 \times 2 - 6 = 6 \) (local minimum).

📌 Therefore, \( a = 2 \).

📌 A circle is inscribed in a square with a side length of 10 units. What is the area of the shaded region between the circle and the square?

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