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Home » \( D(1) = p + q + r + s = 3 \) - inBeat

\( D(1) = p + q + r + s = 3 \) - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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f'(x) = rac{d}{dx}(5x^3 - 15x^2 + 10x) = 15x^2 - 30x + 10
Next, we set the derivative equal to zero to find the critical points:
15x^2 - 30x + 10 = 0
Divide the entire equation by 5:
Using the quadratic formula \( x = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \...
x = rac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 3 \cdot 2}}{2 \cdot 3} = ra...
Simplify \( \sqrt{12} = 2\sqrt{3} \):
x = rac{6 \pm 2\sqrt{3}}{6} = 1 \pm rac{\sqrt{3}}{3}
Thus, the critical points are:
oxed{1 + rac{\sqrt{3}}{3}, 1 - rac{\sqrt{3}}{3}}

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