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Discover How Fearfully and Wonderfully Made Changes Your Perspective Forever! - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 A companyâs profit \( P \) is given by \( P(x) = -5x^2 + 150x - 1000 \), where \( x \) is the number of units sold. Find the number of units sold to maximize profit.

📌 The vertex \( x \)-coordinate is \( x = -rac{b}{2a} = -rac{150}{-10} = 15 \).

📌 To maximize profit, 15 units should be sold.

📌 The roots of the equation \( x^2 - 6x + 9 = 0 \) are:

📌 Factor as \( (x - 3)^2 = 0 \).

📌 The root is \( x = 3 \) (double root).

📌 Find the derivative of \( f(x) = 3x^3 - 5x^2 + 2x - 7 \) and evaluate it at \( x = 2 \).

📌 The derivative is \( f'(x) = 9x^2 - 10x + 2 \).

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