The Derivative in Graphing and Applications By: Tair Akhmejanov.
Graphing Rational Functions. Example (1) For the following function: determine the intervals of increase/decrease, the intervals of upward/downward concavity,
MAX - Min: Optimization AP Calculus. OPEN INTERVALS: Find the 1 st Derivative and the Critical Numbers First Derivative Test for Max / Min –TEST POINTS.
The Writing Questions on the AP Calculus Exams PRESENTED BY LIN MCMULLIN ‘IOLANI SCHOOL.
Copyright © 2008 Pearson Education, Inc. Chapter 5 Graphs and the Derivative Copyright © 2008 Pearson Education, Inc.
3.4 Concavity and the Second Derivative Test. In the past, one of the important uses of derivatives was as an aid in curve sketching. We usually use a.
Unit 4 Applications of Derivatives. Slide 2 4.1 Critical Number Test Types of Maximums and Minimums Absolute/Global Extreme Values Maximum – Minimum –
ECON 1150, Spring 2013 Lecture 3: Optimization: One Choice Variable Necessary conditions Sufficient conditions Reference: Jacques, Chapter 4 Sydsaeter.
1 Chapter 4 Applications of Derivatives. 2 4.1 Extreme Values of Functions.
