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IPMAT Indore 2022 - QA (SA) Q12 Explanation
December 27, 2024
Explanation:
(26)
F(x) = |x| + 2|x - 1| + |x - 2| + |x - 4| + |x - 6| + 2|x - 10|, x ∈ (-∞, ∞)
Minimum value of f(x) will be obtained at one of the six critical points, which are x = 0, 1, 2, 4, 6, 10.
So, f(0) = 2 + 2 + 4 + 6 + 20 = 30
f(1) = 1 + 1 + 3 + 5 + 18 = 28
f(2) = 2 + 2 + 2 + 4 + 16 = 26
f(4) = 4 + 6 + 2 + 0 + 2 + 12 = 26
f(6) = 6 + 10 + 4 + 2 + 8 = 30
f(10) = 10 + 18 + 8 + 6 + 4 = 46
Thus, minimum value f(x) = 26