Question

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

• 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 three 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 + 1+1.4 = 1.6.
Case III: When $|3.6-x|=0\Rightarrow x=3.6$
Value of f(x) = 1.6 + 1.1 + 0 = 2.7.
Hence the minimum value of f(x) is 1.6 at x = 2.5.