175 The case where nis even can be treated similarly. Exercise 5.6.5. Fixa,b∈Rwitha<b. By Theorem 5.6.8, there exists c ∈(a,b) such that f (b)−f (a) b−a ∈ ∂ f (c) ⊂[0,∞). This implies f (b)−f (a) ≥0 and, hence, f (b) ≥f (a). Therefore, f is monotone increasing on R,
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