The roots of the equation

\(x^3+ax^2+bx+24=0\)

are \(2\), \(3\) and \(p\), where \(p\) is an integer.

(i) Find the value of \(p\).

(ii) Show that \(a=-1\) and find the value of \(b\).

Given that a curve has equation \(y=x^3-x^2+bx+24\), find, using your value of \(b\),

(iii) \(\displaystyle \frac{dy}{dx}\),

(iv) the integer value of \(x\) for which the gradient of the curve is \(2\), and the corresponding value of \(y\).

The coordinates of point \(P\) on the curve are given by the values of \(x\) and \(y\) found in part (iv).

(v) Find the equation of the tangent to the curve at \(P\).