How can I calculate a Polynomial that passes through the origin and a given point (
P) having given tangents at the origin (
Ot) and the given point (
The given point will always be to the right of the origin (
Px > 0). The polynomial should be a function of x (i.e. it moves from left to right).
I believe a 3rd degree polynomial will always fit these constraints, but I'm not certain.
I am looking for a function
f( x, Px, Py, Ot, Pt ) = ? which plots a polynomial for
x, satisfying the four given values.
When x = 0, f() = 0 When x = Px, f() = Py When x = 0, f'() = Ot When x = Px, f'() = Pt