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f(x) =1/(|x + 3| + |x + 1| + |x - 2| + |x -5|)

Source: Spanish Mathematical Olympiad 1975 P7

December 23, 2022

algebraanalytic geometryinequalities

Problem Statement

Consider the real function defined by

f(x) =\frac{1}{|x + 3| + |x + 1| + |x - 2| + |x -5|}

for all

x \in R

. a) Determine its maximum. b) Graphic representation.