2.57: Tangent to a cubic and second intersection

0606/22/O/N/20 — Question 5 · 9 marks

DO NOT USE A CALCULATOR IN THIS QUESTION.

(a)
Find the equation of the tangent to the curve y=x3−6x2+3x+10y = x^{3} - 6x^{2} + 3x + 10 at the point where x=1x = 1.
[4]
(b)
Find the coordinates of the point where this tangent meets the curve again.
[5]