Minimum Value of f(x)

Q.23: In the previous question if t = 7, for how many values of x, f(x) will be minimum?

1. 1
2. 2
3. 4
4. 8

Detailed Solution

When t = 7,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+21|
This expression has two middle terms: |x+9|, |x+12|
The value of f(x) will be minimized when the sum of the two middle terms are minimized
=) |x+9|+ |x+12| should be minimum
This happens when -12 ≤ x ≤ -9, Note that for x = -12, -11, -10, -9 the value of the sum of the middle terms = 3. Therefore, for all 4 values of x, f(x) will have minimum value.
Answer choice (C).


Correct Answer: 4

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