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# Solution for In the Interval (1, 2), Function F(X) = 2 | X − 1 | + 3 | X − 2 | is (A) Increasing (B) Decreasing (C) Constant (D) None of These - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
(a) increasing
(b) decreasing
(c) constant
(d) none of these

#### Solution

(b) decreasing

$\text { Given }: f\left( x \right) = 2\left| x - 1 \right| + 3\left| x - 2 \right|$

$\text { If 1 < x < 2, then }\left| x - 1 \right| = x - 1 .$

$\Rightarrow \left| x - 2 \right| = - \left( x - 2 \right)$

$\text { Now,}$

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

$= 2 \left( x - 1 \right) + 3 \left( - x + 2 \right)$

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

$= - x + 4$

$f'\left( x \right) = - 1 < 0$

$\text { So,}f\left( x \right) \text { is decreasing when 1 < x < 2 } .$

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Solution for question: In the Interval (1, 2), Function F(X) = 2 | X − 1 | + 3 | X − 2 | is (A) Increasing (B) Decreasing (C) Constant (D) None of These concept: Increasing and Decreasing Functions. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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