Historical Note Maria Gaetana Agnesi n 1718-1799 - Milan, Habsburg Empire (now Italy) n Oldest of 21children (3 mothers) n Wealthy (and busy) father n.

Slides:

Advertisements

Similar presentations

3.1 Extrema On An Interval.

Advertisements

Increasing and Decreasing Functions

Business Calculus Extrema. Extrema: Basic Facts Two facts about the graph of a function will help us in seeing where extrema may occur. 1.The intervals.

Chapter 3 Application of Derivatives

Mathematicans By: Cameron Wells. Pictures for Days.

Rogawski Calculus Copyright © 2008 W. H. Freeman and Company Figure 5 illustrates the relationship between the concavity of the graph of y = cos x and.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Extreme Values of Functions Section 4.1.

Increasing and Decreasing Functions and the First Derivative Test.

MTH374: Optimization For Master of Mathematics By Dr. M. Fazeel Anwar Assistant Professor Department of Mathematics, CIIT Islamabad 1.

4.1 Maximum and Minimum Values. Maximum Values Local Maximum Absolute Maximum |c2|c2 |c1|c1 I.

Chapter 5 Graphing and Optimization Section 5 Absolute Maxima and Minima.

First and Second Derivative Test for Relative Extrema

Section 5.1 – Increasing and Decreasing Functions The First Derivative Test (Max/Min) and its documentation 5.2.

The Shape of the Graph 3.3. Definition: Increasing Functions, Decreasing Functions Let f be a function defined on an interval I. Then, 1.f increases on.

Applications of Derivatives

Increasing/ Decreasing

FAMOUS MATHEMATICIANS BY: KATIE BYRD. Aryabhatta Born in India.

What would you do: If you woke up and your math homework was miraculously completed? If you could speak more than five different languages? If your parents’

CONCAVITY AND SECOND DERIVATIVE RIZZI – CALC BC. WARM UP Given derivative graph below, find a. intervals where the original function is increasing b.

EXTREMA ON AN INTERVAL Section 3.1. When you are done with your homework, you should be able to… Understand the definition of extrema of a function on.

Applications of Differentiation Calculus Chapter 3.

The textbook gives the following example at the start of chapter 4: The mileage of a certain car can be approximated by: At what speed should you drive.

3 Copyright © Cengage Learning. All rights reserved. Applications of Differentiation.

3-1:Extrema On An Interval Objectives : Find extreme values (maximums and minimums) of a function Find and use critical numbers ©2002 Roy L. Gover (

3.1 Extrema On An Interval.

Learning Target: I will determine if a function is increasing or decreasing and find extrema using the first derivative. Section 3: Increasing & Decreasing.

3.3: Increasing/Decreasing Functions and the First Derivative Test

3.3 Increasing and Decreasing Functions and the First Derivative Test

3.1 Extrema on an Interval Define extrema of a function on an interval. Define relative extrema of a function on an open interval. Find extrema on a closed.

Using Derivatives to Find Absolute Maximum and Minimum Values

4.3 Derivatives and the shapes of graphs 4.5 Curve Sketching

Chapter 3 Applications of Differentiation Maximum Extreme Values

RELATIVE & ABSOLUTE EXTREMA

First Derivative Test So far…

AP Calculus BC September 22, 2016.

Objectives for Section 12.5 Absolute Maxima and Minima

Do your homework meticulously!!!

4.1. EXTREMA OF functions Rita Korsunsky.

CHAPTER 3 Applications of Differentiation

Section 3.1 Day 1 Extrema on an Interval

Extreme Value Theorem Implicit Differentiation

Section 4.3 Optimization.

AP Calculus AB Chapter 3, Section 1

AP Calculus Honors Ms. Olifer

Extreme Values of Functions

Extreme Values of Functions

Extreme Values of Functions

Self Assessment 1. Find the absolute extrema of the function

AP Calculus March 10 and 13, 2017 Mrs. Agnew

3.1 – Increasing and Decreasing Functions; Relative Extrema

Critical Points and Extrema

5.2 Section 5.1 – Increasing and Decreasing Functions

EXTREMA ON AN INTERVAL Section 3.1.

5.1 Day 2 The Candidate Test / Finding Absolute Extrema on a closed interval

Extrema on an Interval, and Critical Points

Increasing and Decreasing Functions

Increasing and Decreasing Functions and the First Derivative Test

Extreme Values of Functions

Derivatives and Graphing

Using Derivatives to Find Absolute Maximum and Minimum Values

Applications of Derivatives

4.2 Critical Points, Local Maxima and Local Minima

Chapter 12 Graphing and Optimization

Unit 4 Lesson 1: Extreme Values of Functions AP Calculus Mrs. Mongold.

Extreme values of functions

Concavity & the 2nd Derivative Test

Chapter 3 Applications of Differentiation Maximum Extreme Values

Unit 4: Applications of Derivatives

Chapter 4 Graphing and Optimization

Presentation transcript:

Historical Note Maria Gaetana Agnesi n Milan, Habsburg Empire (now Italy) n Oldest of 21children (3 mothers) n Wealthy (and busy) father n She spoke three languages n Writer/Debater of philosophy and natural science n Studied religious books and mathematics n Admired Newton n Learned Calculus from a monk - Ramiro Rampinelli n He encouraged her to write a book on Calculus - She is famous for writing that book in 1748

Increasing and Decreasing Functions (page 290)

Closed and Open Interval Notation (page 291) n There is not universal agreement on derivative interval notation. n The theorem below shows this author’s preference. n AP Exam will accept open or closed notation.

First and Second Derivative Summary Concepts

5.2 Extrema (page ) Relative (Local) Maximum or Minimum Values Absolute (Global) Maximum or Minimum Value

Critical Numbers (page 302)

Critical Numbers Summary (page 300)

Critical Numbers (page 302)

Critical Numbers and Relative Extrema (page 302) Relative Extrema occur at critical numbers. However, not every critical number has a relative extrema.

First Derivative Test (page 302)

Second Derivative Test (page 303)

Homework Problem #3 (page 298)

Homework Problem #4 (page 296)

Homework Problem #5 (page 298)

Homework Problem #6 (page 298)

Homework Problem #7 (page 298)

Example 5a,5b,5c (page 295)

Example 2 (page 303)

Example 3 (page 303)

Example 4 (page 304)