The curve is given by $\frac{d^2 y}{dx^2} = 6x^2 - \frac{4}{x^3}$. Its stationary point is at $(-1, \frac{9}{2})$.
(a)[1]
Determine the type of stationary point at $(-1, \frac{9}{2})$.
(b)[5]
Find the equation of the curve.
(c)[3]
Show that there are no further stationary points on the curve.
(d)[3]
Point $A$ moves along the curve, and the $y$-coordinate of $A$ is rising at 5 units per second. Determine the rate at which the $x$-coordinate of $A$ is increasing at the point where $x = 1$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=-1$ into $\frac{d^2y}{dx^2}$ and conclude that it is a minimum.” …