The function has a local minimum or a local maximum at

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The function f(x)=2∣x∣+∣x+2∣−∣∣x+2∣−2∣x∣∣f(x) = 2|x| + |x+2| - \left||x+2| - 2|x|\right| has a local minimum or a local maximum at x=x = (1) −2-2 (2) −23-\frac{2}{3} (3) 22 (4) 23\frac{2}{3}

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