Theorems · Theorem · real analysis
image_sub_le_mul_sub_of_deriv_le
∀ {f : ℝ → ℝ}, Differentiable ℝ f → ∀ {C : ℝ}, (∀ (x : ℝ), deriv f x ≤ C) → ∀ ⦃x y : ℝ⦄, x ≤ y → f y - f x ≤ C * (y - x)Let f : ℝ → ℝ be a differentiable function. If f' ≤ C, then f grows at most as fast
as C * x, i.e., f y - f x ≤ C * (y - x) whenever x ≤ y.
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- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
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