The diagram shows the curve \(y=4+3x-x^2\) intersecting the positive \(x\)-axis at the point \(A\). The line \(y=mx+8\) is a tangent to the curve at the point \(B\). Find

(i) the coordinates of \(A\),

(ii) the value of \(m\),

(iii) the coordinates of \(B\),

(iv) the area of the shaded region, showing all your working.