Originally Posted by
mr fantastic If those are the answers then the question is wrong.
1. The lines in the answers are NOT perpendicular to the line 4 - x + 2y = 0.
2. Furthermore, since the gradient of the lines in the answer is m = -1, the tangent to the cubic must have gradient m = 1. Solving 3x^2 - 12x -2 = 1 does not give an integer solution for x and therefore cannot lead to the answers.
Re-check the question. If the question is as you say, then the question is wrong. There's nothing more can be done.