f(x) = |x - 1| + |x + 1| + |x + 3| + |x + 5|. Find the least possible value of f(x).
Explanation:
To minimize any expression of the form |x + a| + |x + b| + … we need to find critical points and assume a value of x between the 2 middle critical points.
f(x) = |x - 1| + |x + 1| + |x + 3| + |x + 5|
The critical points are: -5, -3, -1 and 1. The 2 critical points in the middle are -3 and -1, hence we assume a value of x in between -3 and -1. Let x = -2.
∴ f(-2) = |-2 - 1| + |-2 + 1| + |-2 + 3| + |-2 + 5| = 3 + 1 + 1 + 3 = 8
Hence, option (c).
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