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The point on the curve 6 y = 4 x 3 - 3 x 2 , the tangent at which makes an equal angle with the coordinate axes is

Options

  1. A1 , - 1 6
  2. B- 1 , - 7 6
  3. C- 1 2 , - 5 24
  4. D1 2 , - 1 24

Correct answer

C. - 1 2 , - 5 24

Step-by-step solution

6 y = 4 x 3 - 3 x 2 6 d y d x = 12 x 2 - 6 x d y d x = 2 x 2 - x = ± 1 2 x 2 - x - 1 = 0 or 2 x 2 - x + 1 = 0 x - 1 2 x + 1 = 0 or x ∈ ϕ x = 1 , x = - 1 2 Hence, points are 1 , 1 6 and - 1 2 , - 5 24

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