AP Calculus AB Extrema, Inflection Points, and Propagated Error Calculator.

Slides:

Advertisements

Similar presentations

AP Calculus Section 3.4 Concavity and the Second Derivative Test

Advertisements

Section 3.4 – Concavity and the Second Derivative Test

Concavity & the second derivative test (3.4) December 4th, 2012.

Objectives: 1.Be able to determine where a function is concave upward or concave downward with the use of calculus. 2.Be able to apply the second derivative.

Miss Battaglia AP Calculus AB/BC.  Let f be differentiable on an open interval I. The graph of f is concave upward on I if f’ is increasing on the interval.

Maximum and Minimum Value Problems By: Rakesh Biswas

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.

Sec 3.4: Concavity and the Second Derivative Test

Increasing and Decreasing Functions and the First Derivative Test.

1 f ’’(x) > 0 for all x in I f(x) concave Up Concavity Test Sec 4.3: Concavity and the Second Derivative Test the curve lies above the tangentsthe curve.

Section 5.2 – Applications of the Second Derivative.

Concavity and the Second- Derivative Test. 1. Determine the open intervals on which the graph of the function is concave upward or concave downward (similar.

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.

Increasing / Decreasing Test

4.3 How Derivatives Affect the Shape of a Graph. Facts If f ’( x ) > 0 on an interval ( a,b ), then f (x) is increasing on ( a,b ). If f ’( x ) < 0 on.

In this section, we will investigate some graphical relationships between a function and its second derivative.

AP/Honors Calculus Chapter 4 Applications of Derivatives Chapter 4 Applications of Derivatives.

Differentiation. f(x) = x 3 + 2x 2 – 3x + 5 f’(x) = 3x 2 + 4x - 3 f’(1) = 3 x x 1 – 3 = – 3 = 4 If f(x) = x 3 + 2x 2 –

Increasing/ Decreasing

Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.

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,

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

Review for Test 3 Glendale Community College Phong Chau.

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

Chapter Four Applications of Differentiation. Copyright © Houghton Mifflin Company. All rights reserved. 4 | 2 Definition of Extrema.

5.3:Higher Order Derivatives, Concavity and the 2 nd Derivative Test Objectives: To find Higher Order Derivatives To use the second derivative to test.

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 5.3 Connecting f′ and f″ with the graph of f Applications of Derivatives Chapter 5.

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

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

Find all critical numbers for the function: f(x) = (9 - x 2 ) 3/5. -3, 0, 3.

AP CALCULUS AB FINAL REVIEW APPLICATIONS OF THE DERIVATIVE.

§3.4 Concavity Concave Up Concave Down Inflection Points Concavity Changes Concave Up Concave Down.

AP Calculus Chapter 5. Definition Let f be defined on an interval, and let x 1 and x 2 denote numbers in that interval f is increasing on the interval.

4.3 – Derivatives and the shapes of curves

If f(x) is a continuous function on a closed interval x ∈ [a,b], then f(x) will have both an Absolute Maximum value and an Absolute Minimum value in the.

Ch. 5 – Applications of Derivatives

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

Relative Extrema and More Analysis of Functions

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.

Extreme Values of Functions

Algebra II Elements 5.8: Analyze Graphs of Polynomial Functions

Review Problems Sections 3-1 to 3-4

Second Derivative Test

Lesson 13: Analyzing Other Types of Functions

First and Second Derivatives Tests

Lesson 13: Analyzing Other Types of Functions

TOPICS ON CHAPTER 4 TEST: 1

AP Calculus AB Chapter 3, Section 1

4.3 – Derivatives and the shapes of curves

AP Calculus Honors Ms. Olifer

Concavity and the Second Derivative Test

Second Derivative Test

Sec 3.4: Concavity and the Second Derivative Test

MATH 1311 Section 1.3.

Self Assessment 1. Find the absolute extrema of the function

5.3 Using Derivatives for Curve Sketching

Concavity of a Function

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

MATH 1311 Section 1.3.

Derivatives and Graphing

Concavity of a Function

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

Copyright © Cengage Learning. All rights reserved.

Concavity of a Function

Concavity & the second derivative test (3.4)

Concavity & the 2nd Derivative Test

Presentation transcript:

AP Calculus AB Extrema, Inflection Points, and Propagated Error Calculator

1. Identify the open intervals where the function is increasing. A.(−∞, 2.236) B.(−2.236, 2.236) C.(−∞, 3.162) D.(−3.162, 2.236)

2. Find the x value of the relative extrema of f(x) = −4x² + 40x + 4. A.Relative maximum at x = 6 B.Relative minimum at x = 6 C.Relative maximum at x = 5 D.Relative minimum at x = 5

3. Determine the open intervals on which the graph of y = −3x³ + 8x² + 6x − 8 is concave down or concave up. A.concave down (−∞, ∞) B.concave down (−∞,.889) concave up (.889, ∞) C.concave up (−∞, ∞) D.concave up (−∞,.889) concave down (.889, ∞)

4. The measurement of the side of a square floor tile is 20 inches, with a possible error of 1/64 inch. Use differentials to approximate the possible propagated error in computing the area of the square. A.±5/16 square inches B.±1/128 square inches C.±5/8 square inches D.±5/32 square inches