I have a cubic polynomial :
$f(x) = ax^3 + bx^2 + cx + d$,
where $ a, b, c$ and $d$ are known values.
The graph of the function goes through points $(x_0, y_0)$ and $(x_1, y_1)$. Also $x_1 > x_0$ : as shown in this image.
I need to draw this graph between $[x_0, x_1]$ in 2D space using cubic Bezier curves. Point at $(x_0, y_0)$ must be the first control point and point at $(x_1, y_1)$ must be the fourth control point.
How can i find the second and the third control points ($C_0$ and $C_1$ as shown here)? Is it possible?