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AP EAMCET20224 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

If the curves y = x 3 - 3 x 2 - 8 x - 4 and y = 3 x 2 + 7 x + 4 touch each other at a point P then the equation of common tangent at P is

Options

  1. Ax - y + 1 = 0
  2. B2 x - y + 1 = 0
  3. Cx + y + 1 = 0
  4. D2 x + y + 1 = 0

Correct answer

A. x - y + 1 = 0

Step-by-step solution

Equating the two given curveto find of intersection we have, 3 x 2 + 7 x + 4 = x 3 - 3 x 2 - 8 x - 4 ⇒ x 3 - 6 x 2 - 15 x - 8 = 0 ⇒ x + 1 2 x - 8 = 0 Now putting x = - 1 in the y = 3 x 2 + 7 x + 4 equation, we get y = 3 - 7 + 4 = 0 , Now putting x = 8 in the equation y = 3 x 2 + 7 x + 4 we get y = 252 So, the points are 8 , 252 and - 1 , 0 Now for equation of the tangent - First we will find slope d y d x = 6 x + 7 So, at x = - 1   or   8 we get d y d x = 1 or 55 Now finding equation we get, y

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