\( f(x) \) is polynomial function of degree 6 , which satisfies \( ...

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\( f(x) \) is polynomial function of degree 6 , which satisfies
\( \mathrm{P} \) \( \lim _{x \rightarrow 0}\left(1+\frac{f(x)}{x^{3}}\right)^{1 / x}=e^{2} \) and has local maximum at \( x= \)

W 1 and local minimum at \( x=0 \) and \( x=2 \). Now, match the following lists and then choose the correct code.
\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ List I } & \multicolumn{1}{|c|}{ List II } \\
\hline a. The coefficient of \( x^{6} \) & p. 0 \\
\hline b. The coefficient of \( x^{5} \) & q. 2 \\
\hline c. The coefficient of \( x^{4} \) & r. \( -\frac{12}{5} \) \\
\hline d. The coefficient of \( x^{3} \) & s. \( \frac{2}{3} \) \\
\hline
\end{tabular}
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