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COMEDK2024MathematicsApplication of Derivatives

The slope of the tangent to the curve, y=x^3-3 x^2 y at (1,1) is

Options

  1. A1 3
  2. B-3
  3. C-1 3
  4. D3

Correct answer

D. 3

Step-by-step solution

We have, y=x^3-3 x^2 y ....(i) Differentiate Eq. (i) w.r.t. x aligned d y d x & =3 x^2-3 (2 x y-x^2 d y d x ) d y d x & =3 x^2-6 x y+3 x^2 d y d x aligned aligned d y d x -3 x^2 d y d x & =3 x^2-6 x y d y d x (1-3 x^2 ) & =3 x^2-6 x y d y d x & = 3 x^2-6 x y 1-3 x^2 aligned Put x=1 and y=1 aligned & & [ d y d x ]_ (1, 1) & = 3-6 1-2 & & [ d y d x ]_ (1, 1) & =3 aligned

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