MathDB

Let

a<a'<b<b'

be real numbers and let the real function

f

be continuous on the interval

[a,b']

and differentiable in its interior. Prove that there exist

c \in (a,b), c'\in (a',b')

such that f(b)\minus{}f(a)\equal{}f'(c)(b\minus{}a), f(b')\minus{}f(a')\equal{}f'(c')(b'\minus{}a'), and

c<c'

. B. Szokefalvi Nagy

Problem Statement