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Question
The minimum value of f(x)=|3−x|+|2+x|+|5−x| is
The minimum value of f(x)=|3−x|+|2+x|+|5−x| is
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Solution
The correct option is B 7
if −∞<x≤−2
f(x)=(3−x)−(2+x)+(5−x)=6−2x
if −2<x≤3
f(x)=(3−x)+(2+x)+(5−x)=10−x
if 3<x≤5
f(x)=−(3−x)+(2+x)+(5−x)=x+4
if 5<x<∞
f(x)=−(3−x)+(2+x)−(5−x)=3x−6
Clearly maximum value of f(x) is 7 at x=3
if −∞<x≤−2
f(x)=(3−x)−(2+x)+(5−x)=6−2x
if −2<x≤3
f(x)=(3−x)+(2+x)+(5−x)=10−x
if 3<x≤5
f(x)=−(3−x)+(2+x)+(5−x)=x+4
if 5<x<∞
f(x)=−(3−x)+(2+x)−(5−x)=3x−6
Clearly maximum value of f(x) is 7 at x=3
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