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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
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