Let $f$ be a function that has derivatives of all orders on the open interval $(2.5, 3.5)$. Assume that $f(3)=7$, $f'(3)=−3$, $f''(3)=12$ and $|f'''(x)≤36|$ for all $x$ in the interval $(2.5, 3.5)$.
Let $h(x)$ be a function that has the properties $h(3)=−2$ and $h'(x)=f (x)$. Find the Maclaurin series for $h(x)$. (Write as many non-zero terms as possible).
Would the series simply be $-2+7(x-3)-\frac{3}{2!}(x-3)^2+\frac{12}{3!}(x-3)^3+...$?
I think that there is a mistake here. A Maclaurin series is centered about $x=0$, so how is it possible to find such a series with only information about $x=3$?
Disclaimer
This is a homework assignment that I think might have a mistake in it. I am not asking for the answer, but instead to know if there is a mistake. If there is no mistake, then I would like to know why not.