Question

Let f(x) = |x - 2| + | 2.5 - x| + |3.6 - x|, where x is a real number attains a minimum at (CAT 2003)

• A. x = 2.3
• B. x = 2.5
• C. x = 2.7
• D. None of these

Answer 1

The correct option is B x = 2.5

f(x) = | x – 2| + | 2.5 – x | + | 3.6 – x | can attain minimum value when either of the terms = 0.

Case I :

When | x – 2 | = 0 $\Rightarrow$ x = 2, value of f(x) = 0.5 + 1.6 = 2.1.

Case II:

When | 2.5 – x | = 0 $\Rightarrow$ x = 2.5
Value of f(x) = 0.5 + 0 + 1.1 = 1.6.

Case III:

When | 3.6 – x | = 0 $\Rightarrow$ x = 3.6

f(x) = 1.6 + 1.1 + 0 = 2.7.
Hence the minimum value of f(x) is 1.6 at x = 2.5.