Question: Prove by differentiation that, for continuous X with continuous density f (x) > 0 such that the expected values below exist, with m the median

Prove by differentiation that, for continuous X with continuous density f (x) > 0 such that the expected values below exist, with m the median and c not a median, E(|X − c|) > E(|X − m|), that is, minc E(|X − c|) occurs only at the median.

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