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Home » First, apply the quotient rule for derivatives: - Leaselab

First, apply the quotient rule for derivatives: - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Using \( \pi \approx 3.14159 \), \( V \approx 45 \times 3.14159 = 141.37155 \) cubic meters.

📌 Solve for \( x \) in the equation \( 2x^2 - 4x - 6 = 0 \).

📌 Use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 2 \), \( b = -4 \), \( c = -6 \).

📌 \( x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4} \).

📌 Solutions are \( x = \frac{4 + 8}{4} = 3 \) and \( x = \frac{4 - 8}{4} = -1 \).

📌 A company produces widgets that sell for $15 each. The cost to produce \( x \) widgets is given by \( C(x) = 5x + 200 \). How many widgets must be sold to break even?

📌 Revenue from selling \( x \) widgets is \( 15x \).

📌 Break-even occurs when revenue equals cost: \( 15x = 5x + 200 \).

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