a, Ta có :
\(A=2\left|3x-2\right|-1\)
Mà \(\left|3x-2\right|\ge0\)
\(\Leftrightarrow2\left|3x-2\right|\ge0\)
\(\Leftrightarrow A=2\left|3x-2\right|-1\ge-1\)
Dấu "=" xảy ra khi :
\(\left|3x-2\right|=0\)
\(\Leftrightarrow3x-2=0\)
\(\Leftrightarrow x=\dfrac{2}{3}\)
Vậy GTNN của A = -1 khi \(x=\dfrac{2}{3}\)
b, Ta có :
\(B=5\left|1-4x\right|-1\)
Mà \(\left|1-4x\right|\ge0\)
\(\Leftrightarrow5\left|1-4x\right|\ge0\)
\(\Leftrightarrow B=5\left|1-4x\right|-1\ge-1\)
Dấu "=" xảy ra khi :
\(\left|1-4x\right|=0\)
\(\Leftrightarrow1-4x=0\)
\(\Leftrightarrow x=\dfrac{1}{4}\)
Vậy B đạt GTNN = -1 khi x = 1/4
c, ta có :
\(C=x^2+3\left|y-2\right|-1\)
Mà \(\left\{{}\begin{matrix}x^2\ge0\\3\left|y-2\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow x^2+3\left|y-2\right|\ge0\)
\(\Leftrightarrow C=x^2+3\left|y-2\right|-1\ge-1\)
Dấu "=" xảy ra khi :
\(\left\{{}\begin{matrix}x^2=0\\3\left|y-2\right|=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)
Vậy C đạt GTNN khi \(\left\{{}\begin{matrix}x=0\\y=2\end{matrix}\right.\)
d, Ta có :
\(D=x+\left|x\right|\)
Mà \(\left|x\right|\ge0\)
\(\Leftrightarrow D=x+\left|x\right|\ge0\)
Dấu "=" xảy ra khi :
\(\left|x\right|=0\)
\(\Leftrightarrow x=0\)
Vậy D đạt GTNN = 0 khi x = 0