Assignment:
The curve C has equation: y = x3 - 2x2 - x + 9, x>0
The point P has coordinates (2,7).
(a) Show that P lies on C.
(b) Find the equation of the tangent to C at P, giving your answer in the form of y = mx+c, where m and c are constants.
The point Q also lies on C.
Given that the tangent to C at Q is perpendicular to the tangent to C at P,
(c) Show that the x-coordinate of Q is 1/3(2+sqrt(6)).
Provide complete and step by step solution for the question and show calculations and use formulas.