2.17: Tangent to a cubic and second intersection

0606/21/O/N/16 — Question 5 · 8 marks

The curve with equation y=x3+2x2−7x+2y = x^{3} + 2x^{2} - 7x + 2 passes through the point A(−2,16)A(-2, 16).
(i)
Find the equation of the tangent to the curve at the point AA.
[3]
(ii)
Find the coordinates of the point where this tangent meets the curve again.
[5]