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NDA 2019 Maths · Mathematics · Application of Derivatives · medium

The tangent to the curve y=x^3-3x+1 is parallel to the line y=9x+4 at the point with positive abscissa. The point is

Single correct option

The tangent to the curve y=x3−3x+1y=x^3-3x+1 is parallel to the line y=9x+4y=9x+4 at the point with positive abscissa. The point is
  1. A. (−2,−1)(-2,-1)
  2. B. (3,19)(3,19)
  3. C. (1,−1)(1,-1)
  4. D. (2,3)(2,3)
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Answer: (D) (2,3)(2,3)

The slope of the tangent is 3x2−33x^2-3, which should equal 99: x2=4x^2=4, so x=±2x=\pm2. The positive value is x=2x=2 and y=8−6+1=3y=8-6+1=3, giving (2,3)(2,3). The point (−2,−1)(-2,-1) also has slope 99 but has negative abscissa; (3,19)(3,19) has slope 2424.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake