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

Operation research, advantages of vogel''s approximation method over north ...

advantages of vogel''s approximation method over north west corner method

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Find the original average of boys and girls in the class, When 6 boys were ...

When 6 boys were admitted & 6 girls left the percentage of boys increased from 60% to 75%. Find the original no. of boys and girls in the class. Ans: Let the no. of Boys be x

Limits, evaluate limit as x approaches 0 (x squared times sin (1/x)

evaluate limit as x approaches 0 (x squared times sin (1/x)

Integration-mathematics, Integration Integration is the reversal of di...

Integration Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical v

Mean is 8.32 find the median, In a frequency distribution mode is 7.88, mea...

In a frequency distribution mode is 7.88, mean is 8.32 find the median.  (Ans: 8.17) Ans:  Mode = 3 median - 2 mean 7.88 = 3 median - 2 x 8.32 7.88 +16.64 = 3 median

The Bake Sale, Lindy has 48 chocolate chip cookies and 64 vanilla wafer coo...

Lindy has 48 chocolate chip cookies and 64 vanilla wafer cookies. How many bags can Lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bag? She pl

How to converting fractions to decimals explain with example, How to Conver...

How to Converting Fractions to Decimals explain with example? To convert fractions to decimals, divide the numerator by the denominator. The quotient is the decimal. Ex

Dilemmas of america''s minority groups, Explain this statement " As we begi...

Explain this statement " As we begin the 21st century, the dilemmas of America's minority groups remain perhaps the primary unresolved domestic issue facing the nation." How might

Area of an ellipse, You know the experation for the area of a circle of rad...

You know the experation for the area of a circle of radius R. It is Pi*R 2 . But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major

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