Calculus I – Lecture 11 Intermediate Value Theorem & Extreme Value Theorem
Автор: Shadi M. Shaqaqha
Загружено: 2026-02-27
Просмотров: 7
Описание:
In this lecture, we study two fundamental results in Calculus:
• The Intermediate Value Theorem (IVT)
• The Extreme Value Theorem (EVT)
We explore:
The geometric meaning of the IVT
Existence of roots using continuity
Applications to polynomial and rational functions
Bounded functions
Conditions required for the EVT (closed and bounded intervals)
Why the hypotheses of EVT are essential
Several illustrative sketch problems
These theorems are essential tools for existence proofs in calculus and form the bridge toward differential calculus.
Instructor: Prof. Shadi Shaqaqha
Department of Mathematics – Yarmouk University
شرح مبرهنتي القيمة المتوسطة والقيم القصوى مع تطبيقات ورسوم توضيحية.
00:00 Intermediate Value Theorem (Statement & Idea)
02:06 IVT – Polynomial Example
03:54 IVT – Equation with Radical
10:03 IVT – Rational Function Example
12:35 Bounded Functions
15:37 Extreme Value Theorem (Statement)
17:43 Sketch Examples & Counterexamples
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