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BITSAT2013MathematicsApplication of DerivativesActual

The equation of all lines having slope 2 which are tangent to the curve y= 1 x-3 , x 3, is

Options

  1. Ay=2
  2. By=2 x
  3. Cy=2 x+3
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The equation of the given curve is y = 1 x -3 , x 3 The slope of the tangent to the given curve at any point ( x , y ) is given by dy dx = -1 ( x -3)² For tangent having slope 2, we must have 2= -1 (x-3)² 2(x-3)²=-1 (x-3)²=- 1 2 which is not possible as square of a real number cannot be negative. Hence, there is no tangent to the given curve having slope 2 .

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