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AP EAMCET2004MathematicsApplication of Derivatives

A particle moves along the curve y=x^2+2 x . Then, the point on the curve such that x and y coordinates of the particle change with the same rate is

Options

  1. A(1,3)
  2. B( 1 2 , 5 2 )
  3. C(- 1 2 ,- 3 4 )
  4. D(-1,-1)

Correct answer

C. (- 1 2 ,- 3 4 )

Step-by-step solution

Given equation of curve is y=x^2+2 x On differentiating both sides w.r.t. t , we get d y d t =(2 x+2) d x d t aligned & & 2 x & =-1 & & x & =-1 / 2, y=-3 / 4 aligned Point on the curve is (- 1 2 ,- 3 4 ) .

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