Question
Download Solution PDFIf f(x) = |x + 1| + |x + 10|, then find the minimum value of f(x).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
f(x) = |x + 1| + |x + 10|
|x + 1| = 0 then x = -1
|x + 10| = 0 then x = -10
f(x) can be zero when x = -1 or x = -10
f(-1) = |-1 + 1| + |-1 + 10| = 9
f(-10) = |-10 + 1| + |-10 + 10| = 9
∴ Minimum value of f(x) = 9 at x = -1 or x = -10
Important Points
If f(x) = |x + a| + |x + b| then
|x + a| and |x + b| = 0
they can be individually zero but can not be zero at same time.
Last updated on Jun 13, 2025
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