Find a 4th degree polynomial approximation for $f(x)=\cos(x)$ near $x = 0$ by producing a polynomial $p(x)=a+bx+cx^2+dx^3+fx^4$ for which $p^j (0)=f^j (0)$ for $0\leq j\leq4$.
This should be solved with calculus at the AB/BC level.
I have no idea where I'm going with this. Help!! Thank you!