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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions1 Mark
MCQ
In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is:
  • A
    Increasing.
  • ✓
    Decreasing.
  • C
    Constant.
  • D
    None of these.
✓

Answer

Correct option: B.
Decreasing.
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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