7

Part of 1975 Spain Mathematical Olympiad

Problems(1)

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

Source: Spanish Mathematical Olympiad 1975 P7

Consider the real function defined by

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

x \in R

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

algebraanalytic geometryinequalities