4.
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.
(1)
(b) Find the equation of the tangent to C at P, giving your answer in the form 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 Qis (2 + √6)
(5)
(5)
(Total 11 marks)
