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x-2-3x-4-x-4-find-min-and-max-




Question Number 207487 by hardmath last updated on 17/May/24
∣x^2  − 3x − 4∣ = ∣x − 4∣  find:   min  and  max  =  ?
$$\mid\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:−\:\mathrm{4}\mid\:=\:\mid\mathrm{x}\:−\:\mathrm{4}\mid \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{max}}\:\:=\:\:? \\ $$
Answered by A5T last updated on 17/May/24
∣x−4∣∣x+1∣=∣x−4∣⇒∣x−4∣=0 or ∣x+1∣=1  ⇒x−4=0 or x+1=1 or x+1=−1  ⇒x=4 or 0 or −2⇒ min=−2; max=4
$$\mid{x}−\mathrm{4}\mid\mid{x}+\mathrm{1}\mid=\mid{x}−\mathrm{4}\mid\Rightarrow\mid{x}−\mathrm{4}\mid=\mathrm{0}\:{or}\:\mid{x}+\mathrm{1}\mid=\mathrm{1} \\ $$$$\Rightarrow{x}−\mathrm{4}=\mathrm{0}\:{or}\:{x}+\mathrm{1}=\mathrm{1}\:{or}\:{x}+\mathrm{1}=−\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{4}\:{or}\:\mathrm{0}\:{or}\:−\mathrm{2}\Rightarrow\:{min}=−\mathrm{2};\:{max}=\mathrm{4} \\ $$
Commented by hardmath last updated on 17/May/24
thank you professor
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{professor} \\ $$

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