The explanation for the correct answer.
Solve for the range where the function $y=-x^{2}+6 x-3$ is increasing.
$
y=-x^{2}+6 x-3
$
Differentiating with respect to $x$, we get
$
\begin{array}{l}
y \prime=-2 x+6 \\
y \text { is increasing if } y \prime>0 \\
\Rightarrow-2 x+6>0 \\
\Rightarrow-2 x>-6 \\
\Rightarrow 2 x<6 \\
\Rightarrow x<3
\end{array}
$