2.51: Tangent to a quadratic and shaded area

0606/22/O/N/17 — Question 11 · 12 marks

2.51 diagram
The diagram shows the curve y=4+3xx2y = 4 + 3x - x^{2} intersecting the positive xx-axis at the point AA. The line y=mx+8y = mx + 8 is a tangent to the curve at the point BB. Find
(i)
the coordinates of AA,
[2]
(ii)
the value of mm,
[3]
(iii)
the coordinates of BB,
[2]
(iv)
the area of the shaded region, showing all your working.
[5]