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
Monotonically increasing.
✓
Monotonically decreasing.
C
Not monotonic.
D
Constant.

✓

Answer

Correct option: B.

Monotonically decreasing.

$f(x) = 2|x - 1| + 3|x - 2|$
$\text{x}\in(1,2)$
$x > 1$ and $x < 2$
$\Rightarrow x - 1 > 0$ and $x - 2 < 0$
$\Rightarrow f(x) = 2|x - 1| + 3|x - 2|$
$\Rightarrow f(x) = 2(x - 1) - 3(x - 2)$
$\Rightarrow f(x) = 2x - 2 - 3x + 6$
$\Rightarrow f(x) = -x + 4$
$\Rightarrow f\ '(x) = -1$
Hence, function is monotonically decreasing.

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