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

Question

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

Monotonically increasing.
Monotonically decreasing.
Not monotonic.
Constant.

✓

Answer

Monotonically decreasing.

Solution:
f(x) = 2|x - 1| + 3|x - 2|
$\text{x}\in(1,2)$
x > 1 and x < 2
⇒ x - 1 > 0 and x - 2 < 0
⇒ f(x) = 2|x - 1| + 3|x - 2|
⇒ f(x) = 2(x - 1) - 3(x - 2)
⇒ f(x) = 2x - 2 - 3x + 6
⇒ f(x) = -x + 4
⇒ f'(x) = -1
Hence, function is monotonically decreasing.

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