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AP EAMCET202418 May 2024Morning ShiftMathematicsApplication of DerivativesActual

A point is moving on the curve y=x^3-3 x^2+2 x-1 and the y -coordinate of the point is increasing at the rate of 6 units per second. When the point is at (2,-1) , the rate of change of x -coordinate of the point is

Options

  1. A3
  2. B1 2
  3. C- 1 2
  4. D-3

Correct answer

A. 3

Step-by-step solution

Since, y=x^3-3 x^2+2 x-1 Now, d y d t =3 x^2 d x d t - 6 x d x d t + 2 d x d t aligned & d y d t = (3 x^2-6 x+2 ) d x d t at (2,-1) & 6=(3 4-6 2+2) d x d t d x d t = 6 2 =3 aligned

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