A curve is given by $y = x^3 + ax^2 + bx + 5$. It has a stationary point at $(1, 9)$.
(a)[5]
Find the values for the constants $a$ and $b$.
(b)[3]
Find the coordinates of the remaining stationary point.
(c)[3]
Point $P$ travels along a section of the curve so that its $y$-coordinate rises at a constant rate of $6$ units per second. Find how fast the $x$-coordinate of $P$ is increasing when $x = 5$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate substitution of the point into $y=ax^3+bx^2+cx+d$” …