Lecture 17 Curve Sketching Last Lectures Summary We

  • Slides: 35
Download presentation
Lecture 17 Curve Sketching

Lecture 17 Curve Sketching

Last Lecture’s Summary We covered Sec 16. 2: Identification of Maxima and Minima •

Last Lecture’s Summary We covered Sec 16. 2: Identification of Maxima and Minima • Relative Extrema (maxima and minima) • Absolute Maxima and Minima • Critical Points • First and Second Derivative Tests for Relative Extrema

Today We will cover sections 16. 3 and 16. 4: • Curve Sketching •

Today We will cover sections 16. 3 and 16. 4: • Curve Sketching • Restricted Domain Considerations • Procedure for Identifying Absolute Maxima and Minima

Curve Sketching functions is facilitated with the information we have acquired in this chapter.

Curve Sketching functions is facilitated with the information we have acquired in this chapter. One can get a feeling for the general shape of the graph of a function without determining and plotting a large number of ordered pairs.

Key Data Points In determining the general shapes of the graph of a function,

Key Data Points In determining the general shapes of the graph of a function, the following attributes are the most significant. • • Relative maxima and minima. Inflection points. x and y intercepts. Ultimate direction

1 - Relative Maxima and Minima •

1 - Relative Maxima and Minima •

2 - Inflection Points •

2 - Inflection Points •

3 - Intercepts •

3 - Intercepts •

4 - Ultimate Direction •

4 - Ultimate Direction •

RESTRICTED-DOMAIN CONSIDERATIONS In this section we will examine procedures for identifying absolute maxima and

RESTRICTED-DOMAIN CONSIDERATIONS In this section we will examine procedures for identifying absolute maxima and minima when the domain of a function is restricted.

II Compute the values of f(x) at the two endpoints of the domain [f(xl)

II Compute the values of f(x) at the two endpoints of the domain [f(xl) and f(xu). III Compare the values of f(x*) for all relevant critical points with (xl) and (xu). The absolute maximum in the largest of these values. The absolute minimum is the smallest of these values.

Step II The values of f (x) at the endpoints of the domain are

Step II The values of f (x) at the endpoints of the domain are

Step III Comparing f (2), f (6), and f (10), we find the absolute

Step III Comparing f (2), f (6), and f (10), we find the absolute minimum of -13 occurs when x = 6 and the absolute maximum of 481/3 occurs when x = 10. The figure presents a sketch of the function.

Review Covered sections 16. 3 and 16. 4: • Curve Sketching • Restricted Domain

Review Covered sections 16. 3 and 16. 4: • Curve Sketching • Restricted Domain Considerations • Procedure for Identifying Absolute Maxima and Minima Next, we’ll start Chapter 17: Application of Optimization.

Sec 4 3 Curve Sketching 1 Curve SketchingSec 4 3 Curve Sketching 1 Curve Sketching
Sec 4 3 Curve Sketching 1 Curve SketchingSec 4 3 Curve Sketching 1 Curve Sketching
Sec 4 3 Curve Sketching 1 Curve SketchingSec 4 3 Curve Sketching 1 Curve Sketching
Chapter 5 Sketching Applications Why Sketching Sketching iChapter 5 Sketching Applications Why Sketching Sketching i
4 3 CURVE SKETCING CURVE SKETCHING To draw4 3 CURVE SKETCING CURVE SKETCHING To draw
CIRCULAR CURVE CIRCULAR CURVE CIRCULAR CURVE Example 1CIRCULAR CURVE CIRCULAR CURVE CIRCULAR CURVE Example 1
Lesson 4 5 Summary of Curve Sketching ObjectivesLesson 4 5 Summary of Curve Sketching Objectives
Lesson 4 6 Summary of Curve Sketching WithLesson 4 6 Summary of Curve Sketching With
Curve Sketching A Summary What Steps Do ICurve Sketching A Summary What Steps Do I
Section 4 5 Summary of Curve Sketching APSection 4 5 Summary of Curve Sketching AP
Section 3 5 Summary of Curve Sketching THINGSSection 3 5 Summary of Curve Sketching THINGS
Summary Curve Sketching Section 4 5 THINGS TOSummary Curve Sketching Section 4 5 THINGS TO
Lesson 4 6 Summary of Curve Sketching WithLesson 4 6 Summary of Curve Sketching With
A SUMMARY OF CURVE SKETCHING Section 3 6A SUMMARY OF CURVE SKETCHING Section 3 6
Sec 4 5 SUMMARY OF CURVE SKETCHING AsymptotesSec 4 5 SUMMARY OF CURVE SKETCHING Asymptotes
Freehand Sketching For Architects 1 Freehand Sketching FreehandFreehand Sketching For Architects 1 Freehand Sketching Freehand
Chapter 5 Sketching Applications Introduction Sketching i eChapter 5 Sketching Applications Introduction Sketching i e
Sketching Vocabulary Chapter 3 4 in Sketching UserSketching Vocabulary Chapter 3 4 in Sketching User
Scribble Sketching Chapter 2 1 in Sketching UserScribble Sketching Chapter 2 1 in Sketching User
Sketching Techniques Purposes of Sketching Think through aSketching Techniques Purposes of Sketching Think through a
Scribble Sketching Chapter 2 1 in Sketching UserScribble Sketching Chapter 2 1 in Sketching User
Sketching an Isometric Circle Introduction to Engineering SketchingSketching an Isometric Circle Introduction to Engineering Sketching
DESIGN TECHNIQUES Design Techniques Sketching Scenarios Stroyboards SketchingDESIGN TECHNIQUES Design Techniques Sketching Scenarios Stroyboards Sketching
Chapter 5 Pictorial sketching Contents Freehand sketching techniquesChapter 5 Pictorial sketching Contents Freehand sketching techniques