CAT Practice : Functions

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Series and Functions

Minimum Value of f(x)

    Q.22: If f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+3t|, where x is an integer and t is a positive integer, find the minimum value of f(x) when t = 6
    1. 63
    2. 36
    3. 30
    4. 25

 

  • Correct Answer
    Choice B. 36

Detailed Solution

When t = 3,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+18|
Minimum value of this function will occur when x = -9 i.e. the middle term is at its minimum which is 0.
Therefore, f(-9) = 9 + 6 + 3 + 0 + 3 + 6 + 9
= 2 x 18
= 36
Answer choice (B).


Correct Answer: 36



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