The minimum value of the function $f (x) = 2 | x - 1 | + | x - 2 |$ is

0

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$1$

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42

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3

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Solution

The correct option is C $1$
$f (x) = 2 | x - 1 | + | x - 2 |$
There are $2$ critical points, $x = 1$ and $x = 2$
$f (1) = 2 \times 0 + 1 = 1$
$f (2) = 2 \times 1 + 0 = 2$
Hence $1$ is the minimum value of $f (x)$

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