Calculus1-Lecture 21|Increasing,Decreasing Functions, Extreme Values, First, Second Derivative Tests скачать в хорошем качестве

Calculus1-Lecture 21|Increasing,Decreasing Functions, Extreme Values, First, Second Derivative Tests

In this lecture, we study increasing and decreasing functions, local and absolute extreme values, and how derivatives help determine the behavior of functions. Topics covered: Increasing, decreasing, and constant functions Local maximum and local minimum Endpoint extrema Absolute maximum and minimum Critical numbers First Derivative Test Extreme Value Theorem (EVT) Applications to polynomial and trigonometric functions Functions with restricted domains Second Derivative Test for classifying extrema Several examples illustrate how derivatives are used to determine intervals of increase/decrease, classify extreme values, and analyze function behavior. Instructor: Prof. Shadi Shaqaqha Department of Mathematics – Yarmouk University شرح الدوال المتزايدة والمتناقصة والقيم العظمى والصغرى باستخدام اختبار المشتقة الأولى والثانية، مع تطبيقات على كثيرات الحدود والدوال المثلثية. 00:00 Increasing, decreasing, and constant functions 05:34 Local maximum and local minimum 09:18 Endpoint extrema 12:21 Absolute maximum and minimum 16:48 First Derivative Test 18:42 Extreme Value Theorem (review) 19:41 Example – Polynomial on a closed interval 26:16 Example – Trigonometric function on [0,2π] 29:25 Behavior at infinity and leading terms 31:56 Example – Polynomial with several critical numbers 40:23 Example – Radical functions and extrema 45:18 Example – Trigonometric extrema problem 50:43 Second Derivative Test 53:10 When the second derivative test fails