Intermediate value theorem, Mathematics

Assignment Help:

Intermediate Value Theorem

Suppose that f(x) is continuous on [a, b] and allow M be any number among f(a) and f(b).   There then exists a number c such that,

1. a < c < b

2. f (c ) = M

All of the Intermediate Value Theorem is actually saying is that a continuous function will take on all values among f(a) & f(b).  Below is a graph of continuous function which illustrates the Intermediate Value Theorem.

2208_Intermediate Value Theorem.png

As we can illustrates from this image if we pick up any value, M, that is among the value of f(a) and the value of f(b) and draw line straight out from this point the line will hit the graph in at least at one point.  In other terms somewhere between a & b the function will take on the value of M.  Also, as the figure illustrates the function might take on the value at more than one place.

It's also significant to note that the Intermediate Value Theorem only says that the function will take on the value of M somewhere among a & b.  It doesn't say just what that value will be.  It just says that it exists.

hence, the Intermediate Value Theorem tells us that a function will take the value of M somewhere among a & b but it doesn't tell us where it will take the value nor does it tell us how several times it will take the value. There is significant idea to remember regarding the Intermediate Value Theorem.

A fine use of the Intermediate Value Theorem is to prove the existence of roots of equations as the given example shows.


Related Discussions:- Intermediate value theorem

Define markov chain, Define Markov chain Random processes with Markov ...

Define Markov chain Random processes with Markov property which takes separate values, whether t is discrete or continuous, are known as Markov chains.

Find out all the critical points for the function, Find out all the critica...

Find out all the critical points for the function. Solution To determine the derivative it's probably simple to do a little simplification previous to we in fact diffe

Simplification, If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?

If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?

3-d geometry, Q) In 3D-geometry give + and - signs for x,y,z, in all eight ...

Q) In 3D-geometry give + and - signs for x,y,z, in all eight octants Ans) There is no specific hard rule for numbering the octants. So, it makes no real sense to ask which octan

Drug administration, A drug is administrated once every four hours. Let D(n...

A drug is administrated once every four hours. Let D(n) be the amount of the drug in the blood system at the nth interval. The body eliminates a certain fraction p of the drug duri

Draw the state diagram - transition function, 1. Let M be the PDA with stat...

1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function δ(q0, a, λ) = {[q0, A]} δ(q0, λ , λ) = {[q1, λ]} δ(q0, b, A) = {[q2

Calculate percentage of increasing customer, Coastal Cable had 1,440,000 cu...

Coastal Cable had 1,440,000 customers within January of 2002. During the first half of 2002 the company launched a large advertising campaign. Through the end of 2002 they had 1,80

What is the area of the court in square feet, A racquetball court is 40 ft ...

A racquetball court is 40 ft through 20 ft. What is the area of the court in square feet? The area of a rectangle is length times width. Thus, the area of the racquetball court

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd