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
Indeed, I would probably just bootstrap my way into the solution by using differentiation all the way.
From , you can immediately conclude that your Thus, your polynomial becomes
Next, you set which implies that
From this equation, you can see that
Rewrite your new polynomial, and continue plugging in the equations you have.
[EDIT]: This I post merely as an alternative to CB's perfectly valid approach.