(B) For $x \in (1, 2)$,we have $x - 1 > 0$ and $x - 2 < 0$. Thus,the function becomes $f(x) = 2(x - 1) - 3(x - 2)$. Simplifying this,$f(x) = 2x - 2 -

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(B) For $x \in (1, 2)$,we have $x - 1 > 0$ and $x - 2 Thus,the function becomes $f(x) = 2(x - 1) - 3(x - 2)$. Simplifying this,$f(x) = 2x - 2 - 3x + 6 = -x + 4$. Now,finding the derivative,$f'(x) = \frac{d}{dx}(-x + 4) = -1$. Since $f'(x) = -1 < 0$ for all $x \in (1, 2)$,the function $f(x)$ is monotonically decreasing in the interval $(1, 2)$.

Class 12 Mathematics Relation and Function Type of Functions based on Mapping

Medium

What is the nature of the function $f(x) = 2 |x - 1| + 3 |x - 2|$ in the interval $(1, 2)$?

A
Monotonically increasing
B
Monotonically decreasing
C
Not monotonic
D
Constant

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Relation and Function

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Type of Functions based on Mapping

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What is the nature of the function $f(x) = 2 |x - 1| + 3 |x - 2|$ in the interval $(1, 2)$?

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