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

Slides:

Advertisements

Similar presentations

All of the planets in our solar system revolve around our sun. Today you will investigate the speeds at which they move around. Orbiting Our Sun.

Advertisements

Class 13: Question 1 Which graph represents an object slowing down, where D is distance and t is time. Assume that units are the same for all four graphs.

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.

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.

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?

5.1 Accumulated Changes Example 1: An objects travels with a velocity of 15 mph. What is the distance traveled after 4 hours t v Distance = area.

Extrema on an interval (3.1) November 15th, 2012.

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

Review Derivatives When you see the words… This is what you know…  f has a local (relative) minimum at x = a  f(a) is less than or equal to every other.

Speed, Velocity and Acceleration What is speed? How is velocity different than speed? What is acceleration? Today’s Goal: Be able to use the proper equations.

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

Product & quotient rules & higher-order derivatives (2.3) October 17th, 2012.

Particle Motion: Total Distance, Speeding Up and Slowing Down THOMAS DUNCAN.

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.

 The act or process of changing position or place Ex: moving vehicles, swinging a bat.

5.3 Definite Integrals, Antiderivatives, and the Average Value of

Increasing & Decreasing Functions & The First Derivative Test (3.3) November 29th, 2012.

Warmup. Be seated before the bell rings DESK homework Warm-up (in your notes) Agenda : go over hw Hw quiz Notes lesson 3.2.

Limits and Continuity Unit 1 Day 4.

If f (x) is continuous over [ a, b ] and differentiable in (a,b), then at some point, c, between a and b : Mean Value Theorem for Derivatives.

Calculus and Analytical Geometry Lecture # 15 MTH 104.

Solving Word Problems Using Kinematics Equations.

Monday, October 12, 2015MAT 145 Please review TEST #2 Results and see me with questions, corrections, and concerns.

Theorems Lisa Brady Mrs. Pellissier Calculus AP 28 November 2008.

Motion. Motion terms and their definitions: position:distance and direction from a reference point motion:change of position over a time interval example:

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.

Speed, Velocity, and Acceleration. Motion What is Motion? Motion is a change in position. Example:

I wonder how mean this theorem really is?

4.2 - The Mean Value Theorem

3.2 Rolle’s Theorem and the

4.2 The Mean Value Theorem State Standard

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

Then  a # c in (a, b) such that f  (c) = 0.

Table of Contents 25. Section 4.3 Mean Value Theorem.

Lesson 3.2 Rolle’s Theorem Mean Value Theorem 12/7/16

PRODUCT & QUOTIENT RULES & HIGHER-ORDER DERIVATIVES (2.3)

1. If you travel at 10mph for 1 hour, how far do you travel?

Increasing & Decreasing Functions & The First Derivative Test (3.3)

Table of Contents 21. Section 4.3 Mean Value Theorem.

HW: Worksheet Aim: How do we solve fractional equation?

Continuity and One-Sided Limits (1.4)

Rolle’s Theorem and the Mean Value Theorem

Sec 2 Cont: Mean Value Theorem (MVT)

Mean Value & Rolle’s Theorems

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

Let’s Calculate….

Rolle’s Theorem.

3.2 Rolle’s Theorem and the

Unit 6 – Fundamentals of Calculus Section 6

30 miles in 1 hour 30 mph 30 miles per hour

Graphing Motion Walk Around

Speed and Velocity Notes

The velocity is constant and the distance is:

1. Be able to apply The Mean Value Theorem to various functions.

A car is decelerated to 20 m/s in 6 seconds

If a 50 kg box has a 200 N force applied to it what is the acceleration?

Total Distance Traveled

Section Net Change in Position/Distance Traveled

An object travels 40 miles in 2 hrs. Calculate its speed?

Rolle’s Theorem and the Mean Value Theorem

Section Net Change in Position/Distance Traveled

The velocity is constant and the distance is:

Intermediate Value Theorem

Mindjog Find the domain of each function..

Do Now: Find all extrema of

Let’s do some cutting!!! G L U E G L U E.

Presentation transcript:

Rolle’s Theorem & the Mean Value Theorem (3.2) October 20th, 2016

I. Rolle’s Theorem Thm. 3.3: 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.

II. The Mean Value Theorem Thm. 3.4: 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 .

Ex. 1: Use the following table of values that models the distance x(t) from Sacramento in miles and velocity v(t) in miles per hour of a train traveling from Sacramento to San Francisco to answer the following questions. Assume that the velocity of the train is a differentiable function on the interval (0,2]. Be sure to justify your reasoning. t 0.3 0.45 0.75 1 1.65 2 x(t) 10 19 42 51 74 90 v(t) 35 39 60 58 85 During the interval (0,2] hours, is there any given time at which the train is neither speeding up nor slowing down? During the interval (0,2] hours, is there any given time at which the velocity of the train is 40 mph? During the interval (0,2] hours, is there any given time at which the acceleration of the train is 70 miles per hour per hour?