Theo đề bài ta có:
\(\left\{{}\begin{matrix}\left|y+1\right|\ge0\Rightarrow\left|y+1\right|^2\ge0\forall y\\\left(z-4\right)^4\ge0\Rightarrow3\left(z-4\right)^4\ge0\forall z\end{matrix}\right.\)
\(\Rightarrow\left|y+1\right|^2+3\left(z-4\right)^4\ge0\)
\(\Rightarrow\left|y+1\right|^2+3\left(z-4\right)^4+5\ge5\)
\(\Rightarrow\dfrac{x}{\left|y+1\right|^2+3\left(z-4\right)^4+5}\le\dfrac{x}{5}\)
Đến đây chỉ tìm được MAX ko có MIN nha bạn
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left|y+1\right|^2=0\Rightarrow y=-1\\3\left(z-4\right)^4=0\Rightarrow z=4\end{matrix}\right.\)
Vậy \(MAX=\dfrac{x}{5}\) khi \(y=-1;z=4\)
