slope — Mathlib

English

The slope of a function f on the interval [a,b] is the vector difference f(b) − f(a) scaled by the inverse of b − a.

Русский

Уклон функции f на промежутке [a,b] – векторная разность f(b) − f(a), домноженная на (b − a)^{-1}.

LaTeX

$$$\operatorname{slope}(f,a,b) = (b-a)^{-1} \cdot (f(b) -\!\!\!\!\!_v f(a))$$$

Lean4

/-- `slope f a b = (b - a)⁻¹ • (f b -ᵥ f a)` is the slope of a function `f` on the interval
`[a, b]`. Note that `slope f a a = 0`, not the derivative of `f` at `a`. -/
def slope (f : k → PE) (a b : k) : E :=
  (b - a)⁻¹ • (f b -ᵥ f a)

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