Curve Sketching Lesson 5.4.

Slides:

Advertisements

Similar presentations

Chapter 5 Graphs and the Derivative JMerrill, 2009.

Advertisements

5.4 Curve Sketching. Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison- Wesley Example 1: Graph the function f given.

What does say about f ? Increasing/decreasing test

2.3 Curve Sketching (Introduction). We have four main steps for sketching curves: 1.Starting with f(x), compute f’(x) and f’’(x). 2.Locate all relative.

Concavity and Rates of Change Lesson 2.5. Changing Rate of Change Note that the rate of change of the curve of the top of the gate is changing Consider.

1 Example 6 Sketch the graph of the function Solution I. Intercepts The x-intercepts occur when the numerator of q(x) is zero i.e. when x=1. The y-intercept.

Section 3.6 – Curve Sketching. Guidelines for sketching a Curve The following checklist is intended as a guide to sketching a curve by hand without a.

Objectives for Section 12.4 Curve Sketching Techniques

Chapter 5 Graphing and Optimization Section 4 Curve Sketching Techniques.

Higher Derivatives Concavity 2 nd Derivative Test Lesson 5.3.

CHAPTER Continuity Derivatives and the Shapes of Curves.

Curve Sketching Lesson 5.4. Motivation Graphing calculators decrease the importance of curve sketching So why a lesson on curve sketching? A calculator.

A Summary of Curve Sketching Lesson 4.6. How It Was Done BC (Before Calculators) How can knowledge of a function and it's derivative help graph the function?

Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.

Curve Sketching 2.7 Geometrical Application of Calculus

A Model Solution and More. Sketch the graph of y = Y- intercepts: For y-intercepts, set x = 0 X- intercepts: For X-intercepts, set y = 0 The x-intercept.

Chapter 4 Day 2. What if the graph has an asymptote or two?? Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes.

Graphing. 1. Domain 2. Intercepts 3. Asymptotes 4. Symmetry 5. First Derivative 6. Second Derivative 7. Graph.

Graphing Rational Functions Objective: To graph rational functions without a calculator.

Using Derivatives to Sketch the Graph of a Function Lesson 4.3.

In the past, one of the important uses of derivatives was as an aid in curve sketching. We usually use a calculator of computer to draw complicated graphs,

Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.

Section 3.5 Summary of Curve Sketching. THINGS TO CONSIDER BEFORE SKETCHING A CURVE Domain Intercepts Symmetry - even, odd, periodic. Asymptotes - vertical,

AP Calculus AB Chapter 3, Section 6 A Summary of Curve Sketching

Curve Sketching. Objective To analyze and sketch an accurate graph of a function. To analyze and sketch an accurate graph of a function.

Graph Sketching: Asymptotes and Rational Functions

Section 2.6 Rational Functions Part 2

Chapter 12 Graphing and Optimization

What does say about f ? Increasing/decreasing test

Summary of Curve Sketching With Calculators

Section 3-6 Curve Sketching.

Analyzing Rational Functions

W-up 3-27 When is the function increasing?

4.3 Using Derivatives for Curve Sketching.

Extreme Values of Functions

4.3 Derivatives and the shapes of graphs 4.5 Curve Sketching

Chapter 2 Applications of the Derivative

Summary Curve Sketching

Section 3.6 A Summary of Curve Sketching

Second Derivative Test

Polynomial and Rational Functions

Chapter 12 Review Important Terms, Symbols, Concepts

Guidelines for sketching the graph of a function

Higher Derivatives Concavity 2nd Derivative Test

Applications of the Derivative

Chapter 12 Graphing and Optimization

Concavity and Second Derivative Test

Concavity and the Second Derivative Test

4.5 An Algorithm for Curve Sketching

Unit 4: curve sketching.

Sec 4.5: Curve Sketching Asymptotes Horizontal Vertical

3.4: Concavity and the Second Derivative Test

5.3 Using Derivatives for Curve Sketching

For each table, decide if y’is positive or negative and if y’’ is positive or negative

AP Calculus BC September 28, 2016.

5.4 Curve Sketching.

Exponential Functions

4.3 Connecting f’ and f’’ with the graph of f

For each table, decide if y’is positive or negative and if y’’ is positive or negative

5. Curve Sketching.

Derivatives and Graphing

55. Graphing Exponential Functions

1 2 Sec4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Graphs of Trigonometric Functions

Concavity and Rates of Change

Chapter 4 Graphing and Optimization

- Derivatives and the shapes of graphs - Curve Sketching

Chapter 4 Graphing and Optimization

Presentation transcript:

Curve Sketching Lesson 5.4

Motivation Graphing calculators decrease the importance of curve sketching So why a lesson on curve sketching? A calculator graph may be misleading What happens outside specified window? Calculator plots, connects points without showing what happens between points False asymptotes Curve sketching is a good way to reinforce concepts of lessons in this chapter

Tools for Curve Sketching Test for concavity Test for increasing/decreasing functions Critical points Zeros Maximums and Minimums

Strategy Determine domain of function Find y-intercepts, x-intercepts (zeros) Check for vertical, horizontal asymptotes Determine values for f '(x) = 0, critical points Determine f ''(x) Gives inflection points Test for intervals of concave up, down Plot intercepts, critical points, inflection points Connect points with smooth curve Check sketch with graphing calculator

Using First, Second Derivatives Note the four possibilities for a function to be … Increasing or decreasing Concave up or concave down Positive (increasing function) Negative (decreasing function) Positive (concave up) Negative (concave down) f '(x) f ''(x)

Try It Out Find as much as you can about the function without graphing it on the calculator

Graphing Without the Formula Consider a function of this description Can you graph it? This function is continuous for all reals A y-intercept at (0, 2)

Assignment Lesson 5.4 Page 354 Exercises 1 – 39 odd