Cho hàm số \(f\left( x \right)={{x}^{4}}-2{{x}^{2}}-2.\) Kí hiệu \(M=\underset{x\in \left[ 0;2 \right]}{\mathop{\max }}\,f\left( x \right), m=\underset{x\in \left[ 0;2 \right]}{\ma...

* Hướng dẫn giải

\(f\left( x \right)={{x}^{4}}-2{{x}^{2}}-2\)

\(D=\mathbb{R}\)

\({f}'\left( x \right)=4{{x}^{3}}-4x=4x\left( {{x}^{2}}-1 \right)\)

\(\Rightarrow {f}'\left( x \right)=0\Leftrightarrow \left[ \begin{align} & x=0 \\ & x=\pm 1 \\ \end{align} \right.\)

\(x=0\Rightarrow f\left( x \right)=-2\).

\(x=1\Rightarrow f\left( x \right)=-3=m\)

\(x=2\Rightarrow f\left( x \right)=6=M\)

\(\Rightarrow M-m=9.\)