imo class 12 application of derivatives

For the curve y = x² - 5x + 6, the tangent at point (2, 0) is parallel to the line:

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For the curve y = x² - 5x + 6, the tangent at point (2, 0) is parallel to the line:

  • A. x - y = 0
  • B. 2x + y = 0
  • C. x - 2y = 0
  • D. x + y = 0

Answer: D) x + y = 0

Explanation: dy/dx = 2x - 5. At x = 2, slope m = 4 - 5 = -1. The line x + y = 0 can be written as y = -x, which has slope -1. Thus, they are parallel.

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