Menu Close

find-minimum-y-2-x-3-4x-2-




Question Number 85248 by jagoll last updated on 20/Mar/20
find minimum  y = 2∣x−3∣ + ∣4x+2∣
$$\mathrm{find}\:\mathrm{minimum} \\ $$$$\mathrm{y}\:=\:\mathrm{2}\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{4x}+\mathrm{2}\mid\: \\ $$
Commented by mr W last updated on 20/Mar/20
x−3=0 ⇒x=3  4x+2=0 ⇒x=−(1/2)  f(3)=∣12+2∣=14  f(−(1/2))=2∣−(1/2)−3∣=7  y_(min) =min(f(3),f(−(1/2)))=7
$${x}−\mathrm{3}=\mathrm{0}\:\Rightarrow{x}=\mathrm{3} \\ $$$$\mathrm{4}{x}+\mathrm{2}=\mathrm{0}\:\Rightarrow{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${f}\left(\mathrm{3}\right)=\mid\mathrm{12}+\mathrm{2}\mid=\mathrm{14} \\ $$$${f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{2}\mid−\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{3}\mid=\mathrm{7} \\ $$$${y}_{{min}} ={min}\left({f}\left(\mathrm{3}\right),{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)\right)=\mathrm{7} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *