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Câu hỏi: Cho hàm số $f\left( x \right)={{x}^{4}}-2{{x}^{2}}-2.$ Kí hiệu $M=\underset{x\in \left[ 0;2 \right]}{\mathop{\max }} f\left( x \right),$ $m=\underset{x\in \left[ 0;2 \right]}{\mathop{\min }} f\left( x \right).$ Khi đó $M-m$ bằng
A. $9$.
B. $5$.
C. $1$.
D. $7$.
A. $9$.
B. $5$.
C. $1$.
D. $7$.
$f\left( x \right)={{x}^{4}}-2{{x}^{2}}-2$.
$D=\mathbb{R}$.
${f}'\left( x \right)=4{{x}^{3}}-4x=4x\left( {{x}^{2}}-1 \right)$.
$\Rightarrow {f}'\left( x \right)=0\Leftrightarrow \left[ \begin{aligned}
& x=0 \\
& x=\pm 1 \\
\end{aligned} \right.$.
$x=0\Rightarrow f\left( x \right)=-2$.
$x=1\Rightarrow f\left( x \right)=-3=m$.
$x=2\Rightarrow f\left( x \right)=6=M$.
$\Rightarrow M-m=9.$
$D=\mathbb{R}$.
${f}'\left( x \right)=4{{x}^{3}}-4x=4x\left( {{x}^{2}}-1 \right)$.
$\Rightarrow {f}'\left( x \right)=0\Leftrightarrow \left[ \begin{aligned}
& x=0 \\
& x=\pm 1 \\
\end{aligned} \right.$.
$x=0\Rightarrow f\left( x \right)=-2$.
$x=1\Rightarrow f\left( x \right)=-3=m$.
$x=2\Rightarrow f\left( x \right)=6=M$.
$\Rightarrow M-m=9.$
Đáp án A.