Đáp án:
$min_A=98 \Leftrightarrow x=\dfrac{1}{10}\\ max_B=\dfrac{5}{3}\Leftrightarrow x=-\dfrac{1}{21}.$
Giải thích các bước giải:
$a)A=\left|2x-\dfrac{1}{5}\right|+98$
Do $\left|2x-\dfrac{1}{5}\right| \ge 0 \ \forall \ x$
$\Rightarrow \left|2x-\dfrac{1}{5}\right|+98 \ge 98 \ \forall \ x\\ \Leftrightarrow A \ge 98 \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow 2x-\dfrac{1}{5}=0 \Leftrightarrow x=\dfrac{1}{10}$
Vậy $min_A=98 \Leftrightarrow x=\dfrac{1}{10}$
$b)B=-\left|3x+\dfrac{1}{7}\right|+\dfrac{5}{3}$
Do $\left|3x+\dfrac{1}{7}\right| \ge 0 \ \forall \ x$
$\Rightarrow -\left|3x+\dfrac{1}{7}\right| \le 0 \ \forall \ x\\ \Rightarrow -\left|3x+\dfrac{1}{7}\right| +\dfrac{5}{3} \le \dfrac{5}{3} \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow 3x+\dfrac{1}{7}=0 \Leftrightarrow x=-\dfrac{1}{21}$
Vậy $max_B=\dfrac{5}{3}\Leftrightarrow x=-\dfrac{1}{21}.$
