Đáp án:
`m∈{-2034;2027}`
Giải thích các bước giải:
`y=|-x^4+8x^2+m|`
`\text(TXĐ: D=R)`
`\text( Đặt f(x))=-x^4+8x^2+m`
`f'(x)=-4x^3+16x`
`f'(x)=0<=>-4x^3+16x=0`
`<=>-4x.(x^2-4)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\x^2-4=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=-2\\x=2\end{array} \right.\)
`\text( Bảng biến thiên:)`
\begin{array}{|c|cc|}\hline \text{$x$}&\text{$-\infty$}&\text{}&\text{-2}&\text{}&\text{-1}&\text{}&\text{0}&\text{}&\text{}&\text{2}&\text{}&\text{3}&\text{}&\text{$+\infty$}\\\hline \text{$f'(x)$}&\text{}&\text{//}&\text{//}&\text{//}&\text{|}&\text{$-$}&\text{0}&\text{}&\text{+}&\text{0}&\text{$-$}&\text{|}&\text{//}&\text{//}\\\hline \text{$f(x)$}&\text{}&\text{}&\text{}&\text{}&\text{m+7}&\text{}&\text{}&\text{}&\text{}&\text{m+16}\\&\text{}&\text{//}&\text{//}&\text{//}&\text{|}&\text{$\searrow$}&\text{}&\text{}&\text{$\nearrow$}&\text{}&\text{$\searrow$}&\text{|}&\text{//}&\text{//}\\&\text{}&\text{}&\text{}&\text{}&\text{}&\text{}&\text{m}&\text{}&\text{}&\text{}&\text{}&\text{ m-9}\\\hline \end{array}
`->max_{[-1;3]}f(x)=f(2)=m+16;min_{[-1;3]}f(x)=f(3)=m-9`
*TH1: `m-9>0<=>m>9`
`->min_{[-1;3]}y=m-9`
`->m-9=2018`
`->m=2027(tmđk)`
*TH2: `m+16<0<=>m<-16`
`->min_{[-1;3]}y=-(m+16)`
`->-(m+16)=2018`
`->-m-16=2018`
`->m=-2034(tmđk)`
`text( Vậy)m∈{-2034;2027}`
