In the interval $(1, 2)$, the function $

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Target Exam

CUET

Subject

Section B1

Chapter

Applications of Derivatives

Question:

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

Options:

strictly increasing.

strictly decreasing.

neither increasing nor decreasing.

remains constant.

Correct Answer:

strictly decreasing.

Explanation:

The correct answer is Option (2) → strictly decreasing. ##

$f(x) = 2|x - 1| + 3|x - 2|$

In $(1, 2)$

$f(x) = +2(x - 1) - 3(x - 2)$

$= 2x - 2 - 3x + 6$

$= -x + 4$

$∵f'(x) = -1$

$f'(x) < 0$

$\Rightarrow f(x)$ is strictly decreasing.