Theorems · Theorem · real analysis
Monotone.convexOn_univ_of_deriv
∀ {f : ℝ → ℝ}, Differentiable ℝ f → Monotone (deriv f) → ConvexOn ℝ Set.univ fIf a function f is differentiable and f' is monotone on ℝ then f is convex.
- Defined in
- Mathlib.Analysis.Convex.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.univstatement and proof · cited by 3,945
- Monotonestatement and proof · cited by 1,397
- interiorproof · cited by 714
- derivstatement and proof · cited by 676
- Continuous.continuousOnproof · cited by 311
- Differentiablestatement and proof · cited by 298
- ConvexOnstatement · cited by 232
- convex_univproof · cited by 53
- Monotone.monotoneOnproof · cited by 43
- Differentiable.differentiableOnproof · cited by 40
- Differentiable.continuousproof · cited by 28
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