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COMEDK2023Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A4 3
  2. B3 2
  3. C3 4
  4. D2 3

Correct answer

C. 3 4

Step-by-step solution

The given equation of the curve is y = x^2 - xy . Differentiating both sides with respect to x , we get: dy dx = 2x - ( y + x dy dx ) Rearranging the terms to solve for dy dx : dy dx + x dy dx = 2x - y dy dx (1 + x) = 2x - y dy dx = 2x - y 1 + x Substituting the point (1, 1 2 ) into the expression for the derivative: . dy dx |_ (1, 1/2) = 2(1) - 1 2 1 + 1 . dy dx |_ (1, 1/2) = 2 - 1 2 2 = 3 2 2 = 3 4 Answer: 3 4

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