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

Determine radicals in exponent form, Evaluate following.               ...

Evaluate following.                √16 and Solution To evaluate these first we will convert them to exponent form and then evaluate that since we already know how to

What is the length of one side of the square, The area of a square is 64 cm...

The area of a square is 64 cm 2 . What is the length of one side of the square? To find out the area of a square, you multiply the length of a side through itself, because all

Sequence and series, Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+.....

Find the sum og series 1+(1+3)+(1+3+5)+.......+(1+3+...+15+17)=

Quadric surfaces - three dimensional spaces, Quadric Surfaces Earlier w...

Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several

Circles, Circles In this section we are going to take a rapid look at ...

Circles In this section we are going to take a rapid look at circles.  Though, prior to we do that we have to give a quick formula that expectantly you'll recall seeing at som

Marketig research report , need help to write Marketing research reprot abo...

need help to write Marketing research reprot about IBM company using spss (statistical program) to analys the given data about the company and write the report according to given i

Correlation and regression, Correlation and Regression Correlation ...

Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

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