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.

Slides:

Advertisements

Similar presentations

We Calculus!!! 3.2 Rolle s Theorem and the Mean Value Theorem.

Advertisements

Rolle’s Theorem By Tae In Ha.

Rolle’s Theorem and The Mean Value Theorem

THE DERIVATIVE AND THE TANGENT LINE PROBLEM

1 Local Extrema & Mean Value Theorem Local Extrema Rolle’s theorem: What goes up must come down Mean value theorem: Average velocity must be attained Some.

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.

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

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

Section 3.2 – Rolle’s Theorem and the Mean Value Theorem

4.2 The Mean Value Theorem.

CHAPTER Continuity Derivatives Definition The derivative of a function f at a number a denoted by f’(a), is f’(a) = lim h  0 ( f(a + h) – f(a))

Rolle’s theorem and Mean Value Theorem ( Section 3.2) Alex Karassev.

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.

SECTION 3.1 The Derivative and the Tangent Line Problem.

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

A car accelerates from a stop to 45 m/sec in 4 sec. Explain why the car must have been accelerating at exactly m/sec at some moment. 2 Do Now.

Lesson 4-2 Mean Value Theorem and Rolle’s Theorem.

5.3 Definite Integrals and Antiderivatives Objective: SWBAT apply rules for definite integrals and find the average value over a closed interval.

APPLICATIONS OF DIFFERENTIATION 4. We will see that many of the results of this chapter depend on one central fact—the Mean Value Theorem.

Chapter Three: Section Two Rolle’s Theorem and the Mean Value Theorem.

Section 5.5 The Intermediate Value Theorem Rolle’s Theorem The Mean Value Theorem 3.6.

Mean Value Theorem for Derivatives4.2. If you drive 100 miles north …in 2 hours… What was your average velocity for the trip? 50 miles/hour Does this.

Rolle’s Theorem/Mean-Value Theorem Objective: Use and interpret the Mean-Value Theorem.

Calculus and Analytical Geometry Lecture # 15 MTH 104.

Section 3.2 Mean Value Theorem Math 1231: Single-Variable Calculus.

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

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.

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.

4.2 The Mean Value Theorem.

3.2 Rolle’s Theorem and the

Rolle’s theorem and Mean Value Theorem (Section 4.2)

Rolle’s Theorem/Mean-Value Theorem

4.2 The Mean Value Theorem State Standard

Hypothesis: Conclusion:

3.2 Rolle’s Theorem and the Mean Value Theorem

Copyright © Cengage Learning. All rights reserved.

Lesson 63 Rolle’s Theorem and the Mean Value Theorem

Table of Contents 25. Section 4.3 Mean Value Theorem.

Rolle’s Theorem Section 3.2.

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

4.4 The Fundamental Theorem of Calculus

Table of Contents 21. Section 4.3 Mean Value Theorem.

Mean Value Theorem for Derivatives

Local Extrema & Mean Value Theorem

Rolle’s Theorem and the Mean Value Theorem

Mean Value & Rolle’s Theorems

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

Rolle’s Theorem.

3.2 Rolle’s Theorem and the

Applications of Derivatives

THE DERIVATIVE AND THE TANGENT LINE PROBLEM

2.1 The Derivative & the Tangent Line Problem

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

Section 3.2 Differentiability.

4.6 The Mean Value Theorem.

Rolle's Theorem Objectives:

The Intermediate Value Theorem

a) Find the local extrema

Warmup 1. What is the interval [a, b] where Rolle’s Theorem is applicable? 2. What is/are the c-values? [-3, 3]

Rolle’s Theorem and the Mean Value Theorem

Unit 5 : Day 6 Linear Approximations,

Intermediate Value Theorem

Rolle’s Theorem and the Mean Value Theorem

Copyright © Cengage Learning. All rights reserved.

Tangent Line Approximations and Theorems

Do Now: Find all extrema of

Copyright © Cengage Learning. All rights reserved.

Presentation transcript:

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

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 Differentiable implies that the function is also continuous.

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 Differentiable implies that the function is also continuous. The Mean Value Theorem only applies over a closed interval.

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 The Mean Value Theorem says that at some point in the closed interval, the actual slope equals the average slope.

Slope of secant: Slope of tangent: Tangent parallel to secant.

Let f (x) be a differentiable function over [ a, b ]. If f(a) = f(b), then there is at least one number, c, in (a,b) such that f ’(c) = 0 Rolle’s Theorem