Science:Math Exam Resources/Courses/MATH110/April 2019/Question 07 (c)/Hint 1

Given a three-times differentiable function $f(x)$ and a point $x=a$, the Taylor polynomial of degree three is a polynomial $P(x)=bx^{3}+cx^{2}+dx+e$ such that $P{\text{ and }}f$ have the same value, first, second and third derivatives at $x=a$. Compare this to Questions 7(a) and 7(b). What similarities do you see in these formulas. Can you think of how noticing these similarities would allow you to answer this question more efficiently in an exam scenario?