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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

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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

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

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

\[ \Rightarrow \left| x - 2 \right| = - \left( x - 2 \right)\]

\[\text { Now,}\]

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

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

\[ = 2x - 2 - 3x + 6\]

\[ = - x + 4\]

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

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

  Is there an error in this question or solution?
Solution 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.
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