## minimize expected value of the absolute difference

Let X be a continuous random variable with median m. Minimize E[|X – b|] as a function of b. Also show that E[|X – b|] = E[|X - m|] + 2 (x - b)fx(x)d(x) where the integral is from b to m.

P.S. How do I find the minimum of the expected value? Can anyone help me please?