Q191 / 270 · NDA 2023 (Phase 1) · Mathematics

Paragraph: Consider the function $f(x)=|x-2|+|3-x|+|4-x|$, where $x \in R$
Question: At what value of $x$ does the function attain minimum value?

  • A
    $2$
  • Correct answer
    B
    $3$
  • C
    $4$
  • D
    $0$

Solution

$f(x)=|x-2|+|3-x|+|4-x|$ $f(2)=0+1+2=3$ $f(3)=1+0+1=2$ $f(4)=2+1+0=3$ $f(0)=2+3+4=9$ $\therefore \quad x=3$ is correct.

Hence, the correct answer is option: 'B'.

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