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Problem 7 - Entrance Test

An Algerian firm’s profit P(x)=–2x³+9x²+12x (x=thousands of units) has maximum profit at x equal to

Correct: C

P′(x)=–6x²+18x+12=0 ⇒ x²–3x–2=0 ⇒ x=(3±√17)⁄2. Positive root ≈3.56, so integer maximum is x=3.