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MHT CET202313 May 2023Evening ShiftMathematicsApplication of DerivativesActual

A (1,-3), B (4,3) are two points on the curve y=x- 4 x . The points on the curve, the tangents at which are parallel to the chord AB , are

Options

  1. A(1,2),(-1,-2)
  2. B(2,0),(-2,0)
  3. C(0,2),(1,-2)
  4. D(3,2),(-3,1)

Correct answer

B. (2,0),(-2,0)

Step-by-step solution

Slope of tangent = slope of AB = 3+3 4-1 = 6 3 =2y=x- 4 x d y ~d x =1+ 4 x^2 aligned & 2=1+ 4 x^2 & x^2=4 & x= 2 aligned When x=2, y=2- 4 2 =0 When x=-2, y=-2+ 4 2 =0 The required points are (2,0) and (-2,0) .

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