Find the points on the curve y = 2×3 + 3×2 − 12x + 3 where the tangent line is horizontal. Smaller X Value and Larger X Value.?

1 Answer

• y = 2x³ + 3x² − 12x + 3

  The tangent line is horizontal when dy/dx = 0 (y’ = 0)

  y’ = 6x² + 6x – 12 = 0 , div by 6

  y’ = x² + x – 2 = 0

  (x – 1)(x + 2) = 0

  x=1 => y = 2*1³ + 3*1² – 12*1 + 3 = -4

  x=-2 => y = 2(-2)³ + 3(-2)² – 12(-2) + 3 = 23

  The tangent points are: (1, -4) and (-2, 23)

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