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

Explanation

To determine whether the function \( f(x) = 2|x-1| + 3|x-2| \) is increasing, decreasing, constant, or none of these in the interval \( (1, 2) \), we will analyze the function step by step.

### Step 1: Simplify the function in the interval \( (1, 2) \)

In the interval \( (1, 2) \):
- \( |x-1| = x-1 \) (since \( x > 1 \))
- \( |x-2| = 2-x \) (since \( x < 2 \))

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