Problem

The equation of a curve is $y=x^3+ax^2+bx+5$. The curve has a stationary point at $(1,9)$.

(a) Find the values of the constants $a$ and $b$.

(b) Find the coordinates of the other stationary point.

(c) A point $P$ is moving along part of the curve in such a way that the $y$-coordinate of $P$ is increasing at a constant rate of 6 units per second.

Find the rate at which the $x$-coordinate of $P$ is increasing when $x=5$.