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Increasing and Decreasing Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIncreasing and Decreasing Functions1 Mark
Question
In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is:
  1. Increasing.
  2. Decreasing.
  3. Constant.
  4. None of these.
✓

Answer

  1. Decreasing.
Solution:
f(x) = 2|x - 1| + 3|x - 2|
In the interval (1, 2)
⇒ |x -1| = x - 1 and |x - 2| = -(x - 2)
⇒ f(x) = 2(x - 1) - 3(x - 2)
⇒ f(x) = -x + 4
⇒ f'(x) = -1
⇒ function is decreasing on (1, 2).

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