The Intermediate Value Theorem
The Intermediate Value Theorem ensures that for a continuous function, any value between its outputs at two points is also achieved somewhere within that interval. It confirms the existence of solutions without pinpointing their exact location.
Peaks and Valleys: A Journey Through the Extreme Value Theorem
The Extreme Value Theorem states that a continuous function defined on a closed interval will always have both a maximum and a minimum value within that interval. This theorem assures the existence of extreme values under the specified conditions of continuity and a bounded domain.
