In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is:

MCQ

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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