150 5.6 Nondifferentiable Convex Functions and Subdifferentials 5.6.3 ▶Let f (x) =∑n k=1|x−k|. Find all absolute minimizers of the function. 5.6.4 Let f : R→Rbe a convex function. Fixa,b∈Rand define the functiongby g(x) =f (ax+b), for x ∈R Prove that ∂g(x0) =a∂ f (ax0 +b). 5.6.5 ▷Let f : R→Rbe a convex function. Suppose that ∂ f (x) ⊂[0,∞) for all x ∈R. Prove that f is monotone increasing on R.
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