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BITSAT2011MathematicsApplication of DerivativesActual

The curve (y-e^ x y +x=0 ) has a vertical tangent at

Options

  1. A((1,1) )
  2. B((0,1) )
  3. C((1,0) )
  4. Dno point

Correct answer

C. ((1,0) )

Step-by-step solution

( aligned & y-e^ x y +x=0 & d y d x -e^ x y (y+x d y d x )+1=0 & i.e., d y d x -y(x+y)-x(x+y) d y d x +1=0 & i.e., [1-x(x+y)] d y d x =y(x+y)-1 aligned ) for the vertical tangents (1-x(x+y)=0 ) i.e., ( y= 1-x^2 x ) ( x =1 ) and ( y =0 )

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