Part 2/7:
Differentiability: The function must be differentiable on the open interval ((a, b)). This prohibits any points in the interval where the derivative does not exist, but does not include the endpoints.
Equal Function Values at the Ends: The values of the function must be equal at these endpoints, expressed as ( f(a) = f(b) ).
When these conditions are met, the theorem guarantees the existence of at least one number ( c ) within the interval ((a, b)) such that the derivative at that point ( f'(c) ) is zero.