For a > b > c > 0, the minimum value of the function f(x) = |x - a| + |x - b| + |x - c| is

For a > b > c > 0, the minimum value of the function f(x) = |x - a| + |x - b| + |x - c| is

We know a > b > c > 0

Let us put x = a in the f(x)

f(x) = |x - a| + |x - b| + |x - c|

f(a) = 0 + a - b + a - c = (a-b)+(a-c)  [ Since, a > b > c > 0]

f(a) = (a-b)+(a-c)  --------(1)

Similarly, put x = b in the f(x)

f(b) = a - b + 0 + b - c  [ Since, a > b so |b - a | = a-b   ]

f(b) = (a - b) + (b - c) = (a - c)   ----------(2)

Similarly, put x = c in the f(x)

f(c) = a - c + b - c + 0 

f(c) = (a-c) + (b-c)    ---------(3)

Comparing (1), (2) and (3)

We can say that (2) is the minimum value.

Thus, the minimum value of the function f(x) = |x - a| + |x - b| + |x - c| is a-c