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AP EAMCET202124 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The point on the curve y=x^3 , at which the tangent to the curve is parallel to the X -axis, is

Options

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

Correct answer

D. (0,0)

Step-by-step solution

Given, curve, y=x^3 Slope of tangent to the curve at any point (x₁, y₁ ) on the curve is = . d y d x |_ (x₁, y₁ ) So, d y d x =3 x^2 Slope of tangent at (x₁, y₁ ) is m_T=3 x₁^2 Tangent is parallel to X -axis m_T= Slope of X -axis array ll & m_T=0 3 x₁^2=0 & x₁=0 y₁=0 array Point of contact is (0,0)

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