Part 3/7:
To better understand the theorem, one can visualize various types of graphs that comply with its rules. For instance, a horizontal line between two points ( a ) and ( b ) indicates that the function values are constant, and thus the derivative is zero for all points in that interval.
In other scenarios, such as a parabolic curve, one can observe a point where the slope (derivative) is zero, affirming the theorem's assertion. Furthermore, the analysis extends to different shapes of functions, whether they open upward or downward, confirming numerous scenarios where multiple points ( c ) meet the criterion ( f'(c) = 0 ).