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BITSAT2023MathematicsApplication of DerivativesActual

The curve given by x+y=e^ x y has a tangent parallel to the Y-axis at the point

Options

  1. A(0,1)
  2. B(1,0)
  3. C(1,1)
  4. DNone of these

Correct answer

B. (1,0)

Step-by-step solution

x+y=e^ x y Differentiating w.r.t. x , we get 1+ d y d x =e^ x y [y+x d y d x ] d y d x (1-x e^ x y )=y e^ x y -1 d y d x = y e^ x y -1 1-x e^ x y d y d x = , as tangent is parallel to Y -axis 1-x e^ x y =0 xe ^ xy =1 This holds, when x=1 and y=0

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