Hello,

I'm preparing for my final exams and I got stuck in a question concerning differentiation:

Let p(x) be a polynomial of degree four whose graph touches the x-axis at the origin and has a horizontal point of inflection at T= (2,2).

Determine p(x).

Well, I understand that the function must be of the form:

p(x) = ax^4 + bx^3 + cx^2 + dx + e

and that

p(0)=0

p'(0)=0

p(2)=2

but how do you know proceed?

I would be very gladful if someone could help me