Statement

Lagrange’s MVT states that if 𝑓: is continuous on [𝑎,𝑏] and differentiable on (𝑎,𝑏), then, for some 𝑐(𝑎,𝑏),

𝑓(𝑐)=𝑓(𝑏)𝑓(𝑎)𝑏𝑎

and (appropriately)

min(𝑎,𝑏)𝑓𝑓(𝑐)max(𝑎,𝑏)𝑓

A more general version of Lagrange’s MVT is Cauchy’s mean value theorem.

References