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Flett's theorem: Given a function

differentiable on

with

, then there is an intermediate point

such that

Geometric interpretation: The secant line connecting the points

and

is exactly the tangent line to the curve

at the point

The example used is the function

on the interval

Reference: T. M. Flett, "A Mean Value Theorem," Math. Gazette, 42, 1958 pp. 38-39.

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Flett's Theorem