Curve \(C\), the red curve, does not look like one of the typical cubic shapes we have seen before. However, it has rotational symmetry about \((0,1)\).
It has some similarities to the curve \(y=x^3+1\) but it does not have the same key feature at \(x=0\).
What are the features of this curve compared to \(y=x^3\) or a translation of it?
We could try to form a set of simultaneous equations to find a cubic equation, but would this be an efficient way to find an equation?
Calculus of curve \(C\)
The curve has no stationary points.
If a cubic curve given by a function \(y=g(x)\) has no stationary points then what do we know about \(g'(x)\)?
After using this resource you could take a look at Can you find… curvy cubics edition.