imo class 12 application of derivatives

A shopkeeper in Mumbai observes that his weekly profit in thousands of rupees from selling x imported watches is given by P(x) = 10 + 2x - x². The number of watches he should sell to maximize profit is:

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A shopkeeper in Mumbai observes that his weekly profit in thousands of rupees from selling x imported watches is given by P(x) = 10 + 2x - x². The number of watches he should sell to maximize profit is:

  • A. 1
  • B. 2
  • C. 3
  • D. 4

Answer: A) 1

Explanation: P'(x) = 2 - 2x = 0 → x = 1. He should sell 1 lot (representing watches as defined by x) to maximize his profit.

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