Let $f$ and $f'$, $f''$, . . . , $f^{(n)}$ be continuous in a closed interval [$a, b$] containing a point $c$. Write down the $n$-th Taylor polynomial of $f(x)$ around $x = c$.
So I know that the Taylor series is $$\sum_{k=0}^{\infty} \frac{f^{(k)}(a)}{k!} (x-a)^k = f(a) + f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^2+...+\frac{f^{(n)}(a)}{n!}(x-a)^n$$
Since this is worth only one mark, I was wondering do I just sub in $x=c$ or am I just not thinking right?
The polynomial you are looking for reads:
$$\sum_{k=0}^{n} \frac{f^{(k)}(c)}{k!} (x-c)^k. $$