Đáp án: A.

Phân tích: Ta có: ${{y}^{/}}=\frac{{{x}^{2}}-2x-3}{{{\left( x-1 \right)}^{2}}}=0\Leftrightarrow \left[ \begin{align}

  & x=-1\notin \left( 2;4 \right) \\

 & x=3\in \left( 2;4 \right) \\

\end{align} \right.$

Ta có: $f\left( 2 \right)=7;\text{ }f\left( 4 \right)=\frac{19}{3};\text{ }f\left( 3 \right)=6\Rightarrow $$\underset{\left[ 2;4 \right]}{\mathop{\min }}\,f\left( x \right)=f\left( 3 \right)=6$.