3.5: Tangent to a cubic and inverse-function gradient

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

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

Find the coordinates of the point of intersection of these two tangents.