AP Calculus Project 4 - Curve Sketching

Similar documents
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B)

5.1 Derivatives and Graphs

2008 AP Calculus AB Multiple Choice Exam

GRAPHING IN POLAR COORDINATES SYMMETRY

100. In general, we can define this as if b x = a then x = log b

AP CALCULUS AB 2008 SCORING GUIDELINES

Math Placement Test Practice Problems

x 2 + y 2 = 1 y 1 = x 2 + 2x y = x 2 + 2x + 1

Pre-Calculus Math 12 First Assignment

Section 2.7 One-to-One Functions and Their Inverses

Ax 2 Cy 2 Dx Ey F 0. Here we show that the general second-degree equation. Ax 2 Bxy Cy 2 Dx Ey F 0. y X sin Y cos P(X, Y) X

Algebra. Exponents. Absolute Value. Simplify each of the following as much as possible. 2x y x + y y. xxx 3. x x x xx x. 1. Evaluate 5 and 123

AP Calculus AB 2007 Scoring Guidelines Form B

Set operations and Venn Diagrams. COPYRIGHT 2006 by LAVON B. PAGE

a cos x + b sin x = R cos(x α)

Section 3.2 Polynomial Functions and Their Graphs

Dear Accelerated Pre-Calculus Student:

RADIUS OF CURVATURE AND EVOLUTE OF THE FUNCTION y=f(x)

AP Calculus AB 2011 Scoring Guidelines

correct-choice plot f(x) and draw an approximate tangent line at x = a and use geometry to estimate its slope comment The choices were:

Calculus AB 2014 Scoring Guidelines

*X100/12/02* X100/12/02. MATHEMATICS HIGHER Paper 1 (Non-calculator) MONDAY, 21 MAY 1.00 PM 2.30 PM NATIONAL QUALIFICATIONS 2012

Average rate of change of y = f(x) with respect to x as x changes from a to a + h:

PRE-CALCULUS GRADE 12

MATHEMATICS FOR ENGINEERING INTEGRATION TUTORIAL 3 - NUMERICAL INTEGRATION METHODS

1. Then f has a relative maximum at x = c if f(c) f(x) for all values of x in some

Calculus 1: Sample Questions, Final Exam, Solutions

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:

Student Performance Q&A:

AP Calculus AB 2005 Scoring Guidelines Form B

AP Calculus AB 2010 Free-Response Questions Form B

Coimisiún na Scrúduithe Stáit State Examinations Commission. Leaving Certificate Examination Mathematics

Objectives. Materials

PRACTICE FINAL. Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 10cm.

Lecture 3 : The Natural Exponential Function: f(x) = exp(x) = e x. y = exp(x) if and only if x = ln(y)

AP Calculus AB 2004 Scoring Guidelines

2.5 Transformations of Functions

USE OF A SINGLE ELEMENT WATTMETER OR WATT TRANSDUCER ON A BALANCED THREE-PHASE THREE-WIRE LOAD WILL NOT WORK. HERE'S WHY.

AP Calculus AB 2011 Free-Response Questions

Investigating Parametric Curves with MATLAB

Calculus 1st Semester Final Review

Mark Howell Gonzaga High School, Washington, D.C.

AP Calculus AB 2004 Free-Response Questions

Lecture 3: Derivatives and extremes of functions

36 CHAPTER 1. LIMITS AND CONTINUITY. Figure 1.17: At which points is f not continuous?

Chapter 7 Outline Math 236 Spring 2001

Friday, January 29, :15 a.m. to 12:15 p.m., only

Math 241, Exam 1 Information.

M Polynomial Functions 1

SOLVING TRIGONOMETRIC INEQUALITIES (CONCEPT, METHODS, AND STEPS) By Nghi H. Nguyen

Polynomials and Polynomial Functions

AP CHEMISTRY 2010 SCORING GUIDELINES (Form B)

AP Calculus AB 2006 Scoring Guidelines

TOPIC 4: DERIVATIVES

The Quadratic Formula

AP Calculus AB Syllabus

6.1. The Exponential Function. Introduction. Prerequisites. Learning Outcomes. Learning Style

Mark Howell Gonzaga High School, Washington, D.C.

Visualizing Differential Equations Slope Fields. by Lin McMullin

Analyzing Piecewise Functions

Algebra II A Final Exam

Write the Equation of the Line Review

f(x) = g(x), if x A h(x), if x B.

Graphs of Polar Equations

x 2 if 2 x < 0 4 x if 2 x 6

*X100/12/02* X100/12/02. MATHEMATICS HIGHER Paper 1 (Non-calculator) NATIONAL QUALIFICATIONS 2014 TUESDAY, 6 MAY 1.00 PM 2.30 PM

Homework # 3 Solutions

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1

MATH 132: CALCULUS II SYLLABUS

Area Under the Curve. Riemann Sums And the Trapezoidal Rule

Analyzing Functions Intervals of Increase & Decrease Lesson 76

SOLUTIONS. Would you like to know the solutions of some of the exercises?? Here you are

DRAFT. Further mathematics. GCE AS and A level subject content

Functions: Piecewise, Even and Odd.

AP Calculus AB First Semester Final Exam Practice Test Content covers chapters 1-3 Name: Date: Period:

MCR3U - Practice Test - Periodic Functions - W2012

ALGEBRA 2/TRIGONOMETRY

AP Calculus BC Exam. The Calculus BC Exam. At a Glance. Section I. SECTION I: Multiple-Choice Questions. Instructions. About Guessing.

Polynomials Past Papers Unit 2 Outcome 1

ab = c a If the coefficients a,b and c are real then either α and β are real or α and β are complex conjugates

AP Calculus BC 2008 Scoring Guidelines

Graphic Designing with Transformed Functions

MATHEMATICS Unit Pure Core 2

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, :15 a.m. to 12:15 p.m.

AP Calculus BC 2013 Free-Response Questions

Colegio del mundo IB. Programa Diploma REPASO The mass m kg of a radio-active substance at time t hours is given by. m = 4e 0.2t.

Notes for EER #4 Graph transformations (vertical & horizontal shifts, vertical stretching & compression, and reflections) of basic functions.

Work, Energy, Conservation of Energy

Section 4.4. Using the Fundamental Theorem. Difference Equations to Differential Equations

Investigating Area Under a Curve

Name Summer Assignment for College Credit Math Courses

MA4001 Engineering Mathematics 1 Lecture 10 Limits and Continuity

ALGEBRA 2/TRIGONOMETRY

Calculus with Parametric Curves

Math 265 (Butler) Practice Midterm II B (Solutions)

Transcription:

AP Calculus Project 4 - Curve Sketching Name You will be in a group of 2 to 4. You will be given a series of s that must be accurately sketched with attention paid to roots, extrema, critical points, inflection points, and end behavior. Grading: Use of class time: 10 points Example Curve: 10 points Guided Practice Curve: 10 points Grab Bag Curve 1 (given f(x)): 10 points Grab Bag Curve 2 (given fʼ(x) & f (x)): 10 points Detail of diagrams: 20 points Explanation of Calculus: 20 points Quality of writing (complete sentences) 10 points Total: 100 points

Part 1 Part 2 Part 3 Part 4 Part 5 Part 6

Curve Sketching part 1 Sketch a complete graph without the calculator. Original #1 f(x) = 3x 2 x 1 Find any red flags in the domain Find the first first using occur

Curve Sketching part 2 Sketch a complete graph without the calculator. Original #2 f(x) = x 3 6x 2 +9x + 1 Find any red flags in the domain Find the first first using occur

Curve Sketching part 3 Sketch a complete graph without the calculator. Original #3 f(x) = 2x 4 + 4x 3 Find any red flags in the domain Find the first first using occur

Curve Sketching part 4 Original #4 Sketch a complete graph without the calculator. f (x) = 1 x 2 Find any red flags in the! domain Find the first first using occur

Curve Sketching part 5 Original #8 Sketch a complete graph without the calculator. f (x) = 6 x 2 " 6 x Find any red flags in the! domain Find the first first using occur

Curve Sketching 6 Original #9 Sketch a complete graph without the calculator. f(x) = sin x + cos x from x = 0 to 2π Find any red flags in the domain Find the first first using occur

2024 © DocPlayer.net Privacy Policy | Terms of Service | Feedback  | Do Not Sell My Personal Information