Cho hàm số $y=f\left( x \right)$ có bảng biến thiên như hình vẽ...

Có $g'\left( x \right)={{\left[ \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right) \right]}^{\prime }}.{f}'\left[ \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right) \right]={f}'\left( x \right)\left( f\left( x \right)-1 \right){f}'\left[ \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right) \right]$
${g}'\left( x \right)=0\Leftrightarrow \left[ \begin{aligned}
& {f}'\left( x \right)=0\Leftrightarrow x=0; x=\dfrac{3}{2} \\
& f\left( x \right)=1\Leftrightarrow x=a \left( a<0 \right) \\
& {f}'\left( \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right) \right)=0.\left( 1 \right) \\
\end{aligned} \right.$
$\left( 1 \right)\Leftrightarrow \left[ \begin{aligned}
& \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right)=0\Leftrightarrow \left[ \begin{aligned}
& f\left( x \right)=0 \\
& f\left( x \right)=2 \\
\end{aligned} \right. \\
& \dfrac{1}{2}{{\left( f\left( x \right) \right)}^{2}}-f\left( x \right)=\dfrac{3}{2}\Leftrightarrow \left[ \begin{aligned}
& f\left( x \right)=3 \\
& f\left( x \right)=-1. \\
\end{aligned} \right. \\
\end{aligned} \right.$
Ta có đồ thị sau
Vậy phương trình ${g}'\left( x \right)=0$ có $7$ nghiệm phân biệt.