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 (Op
)?
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