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