Increasing and Decreasing Functions and the First Derivative Test

Slides:

Advertisements

Similar presentations

Developing the Graph of a Function. 3. Set up a number line with the critical points on it.

Advertisements

Extremum. Finding and Confirming the Points of Extremum.

Sec 3.4: Concavity and the Second Derivative Test

Increasing and Decreasing Functions and the First Derivative Test.

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

Section 4.1 Using First and Second Derivatives. Let’s see what we remember about derivatives of a function and its graph –If f’ > 0 on an interval than.

Concavity f is concave up if f’ is increasing on an open interval. f is concave down if f’ is decreasing on an open interval.

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.

2.1.  Remember that the first derivative test will tell where a function is increasing or decreasing.

Increasing/ Decreasing

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

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

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

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

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

Chapter 4.1 – 4.3 Review Thursday, September 24 Essential Question How do we use differential calculus as a powerful problem-solving tool to analyze graphs.

Increasing/decreasing and the First Derivative test

Increasing, Decreasing, Constant

Calculus Section 4.2 Find relative extrema and graph functions

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/Decreasing Functions and the First Derivative Test

Increasing/ Decreasing Functions

3.3 Increasing and Decreasing Functions and the First Derivative Test

Review Problems Sections 3-1 to 3-4

Graphs and the Derivative

RELATIVE & ABSOLUTE EXTREMA

First Derivative Test So far…

AP Calculus BC September 22, 2016.

3-6 Critical Points and Extrema

CHAPTER 3 Applications of Differentiation

3.3 Increasing and Decreasing Functions and the First Derivative Test

Section 3.1 Day 1 Extrema on an Interval

3. Increasing, Decreasing, and the 1st derivative test

Increasing and Decreasing Functions

Applications of the Derivative

Extrema on an Interval Rizzi – Calc BC.

Sec 3.4: Concavity and the Second Derivative Test

Self Assessment 1. Find the absolute extrema of the function

Concave Upward, Concave Downward

3.1 – Increasing and Decreasing Functions; Relative Extrema

3.1 Extrema on an Interval.

Graphs and the Derivative

Applications of Differentiation

Critical Points and Extrema

5.2 Section 5.1 – Increasing and Decreasing Functions

Chapter 3.3 Increasing and Decreasing Functions and the first derivative test 4.3 Students understand the relation between differentiability and continuity.

More on Functions and Their Graphs

EXTREMA ON AN INTERVAL Section 3.1.

Extrema and the First-Derivative Test

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

Extrema on an Interval, and Critical Points

Open Box Problem Problem: What is the maximum volume of an open box that can be created by cutting out the corners of a 20 cm x 20 cm piece of cardboard?

Increasing and Decreasing Functions

Chapter 3.3 Increasing and Decreasing Functions and the first derivative test 4.3 Students understand the relation between differentiability and continuity.

Increasing and Decreasing Functions and the First Derivative Test

6.5 Using derivatives in graphing

Derivatives and Graphing

(3, 2) 2 -3 (-4, -3) -2 (5, -2) 1. a) Find: f(3) = ______

Packet #14 First Derivatives and Graphs

Chapter 3.3 Increasing and Decreasing Functions and the first derivative test 4.3 Students understand the relation between differentiability and continuity.

Increasing and Decreasing Functions and the First Derivative Test

The First Derivative Test. Using first derivative

Applications of Differentiation

4.2 Critical Points, Local Maxima and Local Minima

Concavity & the second derivative test (3.4)

Applications of the Derivative

Unit 4: Applications of Derivatives

Presentation transcript:

Increasing and Decreasing Functions and the First Derivative Test

1. Identify the open intervals on which the function is increasing or decreasing (similar to p.226 #9-20)

2. Identify the open intervals on which the function is increasing or decreasing (similar to p.226 #9-20)

3. Identify the open intervals on which the function is increasing or decreasing (similar to p.226 #9-20)

4. Identify the open intervals on (0, 2π) on which the function is increasing or decreasing (similar to p.226 #9-20)

5. Identify the open intervals on (0, 2π) on which the function is increasing or decreasing (similar to p.226 #9-20) NEXT TIME SPRING 2013

6. Identify the open intervals on (0, 2π) on which the function is increasing or decreasing (similar to p.226 #9-20)

7. Find the critical numbers of f (if any) 7. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

8. Find the critical numbers of f (if any) 8. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

9. Find the critical numbers of f (if any) 9. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

10. Find the critical numbers of f (if any) 10. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

11. Find the critical numbers of f (if any) 11. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

12. Find the critical numbers of f (if any) 12. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58) NEXT TIME SPRING 2013

13. Find the critical numbers of f (if any) 13. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

14. Find the critical numbers of f (if any) 14. Find the critical numbers of f (if any). Find the open intervals on which the function is increasing or decreasing and locate all relative extrema. Use a graphing utility to confirm your results (similar to p.226 #21-58)

15. Consider the function on the interval (0, 2π) 15. Consider the function on the interval (0, 2π). For each function, (a) find the open interval(s) on which the function is increasing or decreasing. (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results (similar to p.226 #59-66)