Maximum value of the function \(f(x)=3^{1+2x-x^{2}}\) is equal to

\(3\) \(9\) \(27\) \(81\)

\(9\)

\(1+2x+x^{2}\) is a quadratic equation. \(\hspace{10cm}\) \(\begin{aligned}1+2x-x^{2}&=-x^{2}+2x-1+2\\ &=-(x-1)^{2}+2\\ &\leq 2\end{aligned}\hspace{5cm}\) Thus, maximum value of \(f(x)=3^2=9\)