In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is: - Vidyadip

MCQ

In the interval $(1, 2)$, function $f(x) = 2|x - 1| + 3|x - 2|$ is:

A
Increasing.
✓
Decreasing.
C
Constant.
D
None of these.

✓

Answer

Correct option: B.

Decreasing.

$f(x) = 2|x - 1| + 3|x - 2|$
In the interval $(1, 2)$
$\Rightarrow |x -1| = x - 1$ and $|x - 2| = -(x - 2)$
$\Rightarrow f(x) = 2(x - 1) - 3(x - 2)$
$\Rightarrow f(x) = -x + 4$
$\Rightarrow f'(x) = -1$
$\Rightarrow$ function is decreasing on $(1, 2).$

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