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Question Number 208646 by hardmath last updated on 20/Jun/24

y = ∣x − 2∣ + ∣x + 4∣  Find:   min(y)   and   max(y)

$$\mathrm{y}\:=\:\mid\mathrm{x}\:−\:\mathrm{2}\mid\:+\:\mid\mathrm{x}\:+\:\mathrm{4}\mid \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:\:\:\mathrm{and}\:\:\:\mathrm{max}\left(\mathrm{y}\right) \\ $$

Answered by A5T last updated on 20/Jun/24

y has no global maximum,y→+∞ as x→+_− ∞  ∣x−2∣+∣−4−x∣≥∣x−2−4−x∣=6⇒min(y)=6

$${y}\:{has}\:{no}\:{global}\:{maximum},{y}\rightarrow+\infty\:{as}\:{x}\rightarrow\underset{−} {+}\infty \\ $$$$\mid{x}−\mathrm{2}\mid+\mid−\mathrm{4}−{x}\mid\geqslant\mid{x}−\mathrm{2}−\mathrm{4}−{x}\mid=\mathrm{6}\Rightarrow{min}\left({y}\right)=\mathrm{6} \\ $$

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