Скачать или смотреть Calculus I – Lecture 11 Intermediate Value Theorem & Extreme Value Theorem

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