Mean Value Theorem
The Mean Value Theorem states that if are real numbers and the function
is differentiable on the interval
, then there exists a value
in
such that
In words, there is a number in
such that
equals the average value of the function in the interval
.
[b]Proof:[/b]
[b]Other:[/b]
Rolle's Theorem is a sub-case of this theorem. It states that if for two real numbers a and b, then there is a real number c such that
and
.
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