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 → R be a convex function. Fix a,b ∈ R and defne the function g by g(x)= f (ax + b), for x ∈ R Prove that ∂ g(x0)= a∂ f (ax0 + b). 5.6.5 ▷ Let f : R → R be a convex function. Suppose that ∂ f (x) ⊂ [0,∞) for all x ∈ R. Prove that f is monotone increasing on R.
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