Question

The minimum value of f(x) = |x – 1| + |x - 2| + |x - 3| is equal to.

• A. 1
• B. 2
• C. 3
• D. Zero

Answer 1

Answer: (B)

2

Answer 2

We get f(x) =

⇒ f'(x) = $\left\{ \begin{array} { c c } - 3 , & x < 1 \\ - 1 , & 1 < x < 2 \\ 1 , & 2 < x < 3 \\ 3 , & x > 3 \end{array} \right.$

Thus f(x) decreasing for x < 2 and increasing for x > 2. Hence f (x) |_min = f(2) = 2 .