Intermediate Value Theorem

Slides:

Advertisements

Similar presentations

Chapter 2.5  Continuity at a Point: A function is called continuous at c if the following 3 conditions are met.  1) is defined 2) exists 3)  Continuity.

Advertisements

Intermediate Value Theorem. Objectives Students will be able to Determine if the Intermediate Value Theorem Applies to a particular function Use the Intermediate.

1.5 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

Sec 2.5: CONTINUITY. Study continuity at x = 4 Sec 2.5: CONTINUITY Study continuity at x = 2.

4.2 The Mean Value Theorem.

Intermediate Value Theorem If f is continuous on [ a,b ] and k is any number between f(a) and f(b), inclusive, then there is at least one number c in the.

1.4 Continuity and One-Sided Limits This will test the “Limits” of your brain!

Section 1.4: Continuity and One-Sided Limits

Math 1304 Calculus I 2.5 – Continuity. Definition of Continuity Definition: A function f is said to be continuous at a point a if and only if the limit.

Continuity Section 2.3.

MAT 1234 Calculus I Section 1.8 Continuity

10/13/2015 Perkins AP Calculus AB Day 5 Section 1.4.

Miss Battaglia AB/BC Calculus.  What does it mean to be continuous? Below are three values of x at which the graph of f is NOT continuous At all other.

Practice! 1. For the graph shown, which of these statements is FALSE? (A) f(x) is continuous at x=2 (B) (C) (D) (E) f(x) is continuous everywhere from.

Section 2.5 Continuity. CONTINUITY AT A NUMBER a Definition: A function f is continuous at a number a if.

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

CONTINUITY Mrs. Erickson Continuity lim f(x) = f(c) at every point c in its domain. To be continuous, lim f(x) = lim f(x) = lim f(c) x  c+x  c+ x 

2.4 Continuity and its Consequences and 2.8 IVT Tues Sept 15 Do Now Find the errors in the following and explain why it’s wrong:

Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.

1-4: Continuity and One-Sided Limits

1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

2.7: Continuity and the Intermediate Value Theorem Objectives: Define and explore properties of continuity Introduce Intermediate Value Theorem ©2002.

Section 4.2 Rolle’s Theorem & Mean Value Theorem Calculus Winter, 2010.

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

Section 1.4 – Continuity and One-Sided Limits

CONTINUITY. A function f(x) is continuous at a number a if: 3 REQUIREMENTS f(a) exists – a is in the domain of f exists.

Limits and Continuity Unit 1 Day 4.

Continuity and One- Sided Limits (1.4) September 26th, 2012.

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.

AP Calc AB IVT. Introduction Intermediate Value Theorem If a function is continuous between a and b, then it takes on every value between and. Because.

Warm Ups. AP CALCULUS 2.4 Continuity Obj: identify the types of discontinuity.

1.4 Continuity and One-Sided Limits Main Ideas Determine continuity at a point and continuity on an open interval. Determine one-sided limits and continuity.

Calculus 1-4 Continuity and One-Sided Limits. Vocabulary Continuous: A function that is uninterrupted in the given interval None of these is continuous.

AP Calculus AB Objectives: Determine continuity at a point, determine one-sided limits, understand the Intermediate Value Theorem.

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

1.4 Continuity Calculus.

Continuity and One-Sided Limits

Continuity In section 2.3 we noticed that the limit of a function as x approaches a can often be found simply by calculating the value of the function.

4.2 The Mean Value Theorem.

3.2 Rolle’s Theorem and the

4.2 The Mean Value Theorem State Standard

Rolle’s Theorem Section 3.2.

Copyright © Cengage Learning. All rights reserved.

3.7 The Real Zeros of a Polynomial Function

Continuity and One-Sided Limits (1.4)

2.2 Polynomial Function of Higher Degrees

The Sky is the Limit! Or is it?

Rolle’s Theorem.

3.7 The Real Zeros of a Polynomial Function

3.2 Rolle’s Theorem and the

AP Calculus September 6, 2016 Mrs. Agnew

Important Values for Continuous functions

Section 3.2 Differentiability.

Continuity and Intermediate Value Theorem

Continuity and One-Sided Limits

1.4 Continuity and One-Sided Limits (Part 2)

Sec 2.5: Continuity Continuous Function

Rolle's Theorem Objectives:

The Intermediate Value Theorem

Rolle’s Theorem and the Mean Value Theorem

1.4 Continuity and One-Sided Limits This will test the “Limits”

A function f is continuous at the point x = a if the following are true: f(a) a.

Sec 2.5: Continuity Continuous Function

Continuity and One-Sided limits

Lesson 63 - Intermediate Value Theorem

2.3 Continuity.

Presentation transcript:

Intermediate Value Theorem

Removing a Discontinuity Discontinuity at a point can be removed by making up a value for where it is currently discontinuous so that it will be continuous

Example Is the function below continuous everywhere? If not what will make it continuous everywhere?

Intermediate Value Theorem Suppose that f is continuous on the closed interval [a,b] and let M be any number between f(a) and f(b). Then there exists at least number c in [a, b] such that f(c)=M.

Example Show that there is a root of on the interval [1,2]