AP Calculus BC September 23, 2016.

Slides:

Advertisements

Similar presentations

The Mean Value Theorem and Rolles Theorem Lesson 3.2 I wonder how mean this theorem really is?

Advertisements

Rolle’s Theorem and the Mean Value Theorem3.2 Teddy Roosevelt National Park, North Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by.

Aim: Rolle’s Theorem Course: Calculus Do Now: Aim: What made Rolle over to his theorem? Find the absolute maximum and minimum values of y = x 3 – x on.

Miss Battaglia AP Calculus AB/BC.  Sketch a coordinate plane on a piece of paper. Label the points (1,3) and (5,3). Using a pencil, draw the graph of.

AP Calculus AB Chapter 3, Section 2 Rolle’s Theorem and the Mean Value Theorem

Rolle’s Theorem and the Mean Value Theorem. Rolle’s Theorem  Let f be continuous on the closed interval [a, b] and differentiable on the open interval.

Rolle’s and The Mean Value Theorem BC Calculus. Mean Value and Rolle’s Theorems The Mean-Value Theorem ( and its special case ) Rolle’s Theorem are Existence.

Sec. 3.2: Rolle’s Theorem and MVT Rolle’s Theorem: Let f be continuous on the closed interval [a, b] and differentiable on the open interval (a, b). If.

The Mean Value Theorem Lesson 4.2 I wonder how mean this theorem really is?

First Day of School Day 1 8/19/2013 Objectives: Go over the classroom rules and regulations. Go over the syllabus. Discuss expectations and answer questions.

CHAPTER 3 SECTION 3.2 ROLLE’S THEOREM AND THE MEAN VALUE THEOREM

 Exploration:  Sketch a rectangular coordinate plane on a piece of paper.  Label the points (1, 3) and (5, 3).  Draw the graph of a differentiable.

AP Calculus BC September 2, 2015 Day 3 - §1.4 Continuity and One-Sided Limits.

Rolle’s and The Mean Value Theorem BC Calculus. Mean Value and Rolle’s Theorems The Mean-Value Theorem ( and its special case ) Rolle’s Theorem are Existence.

Calculus 1 Rolle’s Theroem And the Mean Value Theorem for Derivatives Mrs. Kessler 3.2.

Calculus Date: 12/10/13 Obj: SWBAT apply Rolle’s and the Mean Value Thm derivatives of absolute.

3.2 Rolle’s Theorem and the Mean Value Theorem. After this lesson, you should be able to: Understand and use Rolle’s Theorem Understand and use the Mean.

EXTREMA ON AN INTERVAL Section 3.1. When you are done with your homework, you should be able to… Understand the definition of extrema of a function on.

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

 On any continuous function between points a and b there exists some point(s) c where the tangent line at this point has the same slope as the secant.

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.

AP Calculus Unit 4 Day 7 Optimization. Rolle’s Theorem (A special case of MVT) If f is continuous on [a,b] and differentiable on (a,b) AND f(b)=f(a) Then.

4.2A Rolle’s Theorem* Special case of Mean Value Theorem Example of existence theorem (guarantees the existence of some x = c but does not give value of.

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.

I wonder how mean this theorem really is?

4.2 - The Mean Value Theorem

3.2 Rolle’s Theorem and the Mean Value Theorem

3.2 Rolle’s Theorem and the Mean Value Theorem

Rolle’s Theorem & the Mean Value Theorem (3.2)

Table of Contents 25. Section 4.3 Mean Value Theorem.

Mean Value and Rolle’s Theorem

Rolle’s Theorem Section 3.2.

AP Calculus BC September 12, 2016.

Table of Contents 21. Section 4.3 Mean Value Theorem.

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

Rolle’s Theorem and the Mean Value Theorem

Rolle’s Theorem and the Mean Value Theorem

Review Problems Sections 3-1 to 3-4

Sketching the Derivative

Sec 2 Cont: Mean Value Theorem (MVT)

Mean Value & Rolle’s Theorems

First Derivative Test So far…

CHAPTER 3 SECTION 3.2 ROLLE’S THEOREM AND THE MEAN VALUE THEOREM

AP Calculus BC September 22, 2016.

Entry Task Consider the function f(x):

AP Calculus November 9-10, 2016 Mrs. Agnew

Continuity and One-Sided Limits

Section 3.1 Day 1 Extrema on an Interval

AP Calculus AB Chapter 3, Section 1

Concavity and the Second Derivative Test

AP Calculus BC September 29, 2016.

AP Calculus BC September 30, 2016.

Day 6 – Tangent Lines and Derivatives

Self Assessment 1. Find the absolute extrema of the function

AP Calculus BC September 28, 2016.

ROLLES THEOREM AND THE EXTREME VALUE THEOREM

AP Calculus March 10 and 13, 2017 Mrs. Agnew

Section 3.2 Calculus AP/Dual, Revised ©2017

EXTREMA ON AN INTERVAL Section 3.1.

3.2 Rolle’s Theorem and the Mean Value Theorem

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?

a) Find the local extrema

Rolle’s Theorem and the Mean Value Theorem

ROLLES THEOREM AND THE EXTREME VALUE THEOREM

3.2: Rolle’s Theorem and the Mean Value Theorem

Section 3.2 Day 1 Mean Value Theorem

Mindjog Find the domain of each function..

Parametric Equations and Eliminating the Parameter

Concavity & the 2nd Derivative Test

Unit 4: Applications of Derivatives

Presentation transcript:

AP Calculus BC September 23, 2016

Entry Task Sketch a rectangular coordinate plane on a piece of paper. Label the points (1, 3) and (5, 3). Use your pencil to draw the graph of a differentiable function f that starts at (1, 3) and ends at (5, 3). Is there at least one point where 𝑓 ′ =0? Is it possible to draw the graph so that there isn’t a point for which 𝑓 ′ =0? Explain your reasoning.

Learning Targets I understand Rolle’s Theorem and the Mean Value Theorem and how they relate to derivatives of functions. I solved a variety of problems involving applications of derivatives with Rolle’s Theorem and the MVT.

Section 3.1 – Extrema on and INterval What are extrema? The Extreme Value Theorem If f is continuous on a closed interval [a, b], then f has both a maximum and a minimum.

Rolle’s Theorem Revisit exit Ticket

Rolle’s Theorem Rolle’s Theorem Let 𝑓 be continuous on the closed interval [𝑎,𝑏] and differentiable on the open interval (𝑎,𝑏). If 𝑓 𝑎 =𝑓(𝑏), then there is at least one number 𝑐 in (𝑎,𝑏) such that : 𝑓 ′ 𝑐 =0.

MVT The Mean Value Theorem If 𝑓 is continuous on the closed interval 𝑎,𝑏 and differentiable on the open interval (𝑎,𝑏), then there exists a number 𝑐 in (𝑎,𝑏) such that: 𝑓 ′ 𝑐 = 𝑓 𝑏 −𝑓 𝑎 𝑏−𝑎

Two stationary patrol cars equipped with radar are 5 miles apart on a highway. As a truck passes the first patrol car, its speed is clocked at 55 mph. Four minutes later, when the truck passes the second patrol car, its speed is clocked at 50 mph. Prove that the truck must have exceeded the speed limit (55 mph) at some time during the four minutes.

Assignment #10 Page 176-178: 15, 17, 21, 41, 44, 59, 64, 77-80