A curve has equation \(y=p(x)\), where

\(p(x)=x^3-4x^2+6x-1.\)

(a) Find the equation of the tangent to the curve at the point \((3,8)\). Give your answer in the form \(y=mx+c\).

(b)

(i) Given that \(p^{-1}\) exists, write down the gradient of the tangent to the curve \(y=p^{-1}(x)\) at the point \((8,3)\).

(ii) Find the coordinates of the point of intersection of these two tangents.