Given the Taylor polynomial for $f(x)$ at $x=3$, find $f^{(4)}(3)$ :
\[
\begin{array}{l}
T_{4}(x)=2+x-3+(x-3)^{2}+(x-3)^{3}-2(x-3)^{4} \\
f^{(4)}(3)=99
\end{array}
\]

Step 1 ：Given the Taylor polynomial for \(f(x)\) at \(x=3\):

Step 2 ：\(T_{4}(x)=2+(x-3)+1(x-3)^{2}+1(x-3)^{3}-2(x-3)^{4}\)

Step 3 ：The coefficients of the Taylor polynomial represent the derivatives of \(f(x)\) at \(x=3\) divided by the corresponding factorial:

Step 4 ：\(f(3) = 2\)

Step 5 ：\(f'(3) = 1\)

Step 6 ：\(f''(3) = 1 \cdot 2\)

Step 7 ：\(f'''(3) = 1 \cdot 3!\)

Step 8 ：\(f^{(4)}(3) = -2 \cdot 4!\)

Step 9 ：Calculate \(f^{(4)}(3)\):

Step 10 ：\(f^{(4)}(3) = -2 \cdot 4! = -2 \cdot 24 = -48\)

Step 11 ：\(\boxed{f^{(4)}(3) = -48}\)