IB Maths AA HL Sl 5 7 Second Derivative and Graph Behaviour Topic Practice

This question investigates a ratio of lengths found from the line passing through the points of inflexion of a quartic curve of the form $y=x^{4}-m x^{3}+n x$.
The curve $y=x^{4}-3 x^{3}+3 x$ has points of inflexion at B and C . The line passing through B and C intersects the curve again at points A and D . This is shown in the following graph.

Find $\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}$.