Remark 2

Tag 0844, permanent. Cite it as [Bourbaki, Tag 0844].

Functions of a Real Variable, chapter I, § 2. THE MEAN VALUE THEOREM

The hypothesis of continuity on $f$ on the closed interval I (and not just right continuity $^4$ at every point of $[a, b[$ ) is essential for the validity of prop. 2 (cf. I, p. 36, exerc. 8 ).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

I, p. 36