imo class 12 application of derivatives

The maximum slope of the curve y = -x³ + 3x² + 9x - 27 is:

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The maximum slope of the curve y = -x³ + 3x² + 9x - 27 is:

  • A. 9
  • B. 0
  • C. 15
  • D. 12

Answer: D) 12

Explanation: Slope m = dy/dx = -3x² + 6x + 9. To maximize m, dm/dx = -6x + 6 = 0 → x = 1. Max slope = -3(1)² + 6(1) + 9 = 12.

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