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

Matrix, cramers rule introduction

cramers rule introduction

Triangles, about scalene,equilateral and isosceles.

about scalene,equilateral and isosceles.

What could the dimensions of the floor be in terms of x, Harold is tiling a...

Harold is tiling a rectangular kitchen floor with an area that is expressed as x 2 + 6x + 5. What could the dimensions of the floor be in terms of x? Because area of a rectang

Sharon purchased six movie tickets how much was each ticket, Sharon purchas...

Sharon purchased six adult movie tickets. She spent $43.50 on the tickets. How much was each ticket? To ?nd out the price of each individual ticket, you should divide the total

How to dividing rational expressions, How to Dividing Rational Expressions ...

How to Dividing Rational Expressions ? To divide two fractions, or rational expressions, keep in Mind that division is the same as multiply by the Reciprocal of the second fra

Using euclid''s algorithm find the value of x & y, If d is the HCF of 30, 7...

If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans:    Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12

Complex numbers, Complex Numbers In the radicals section we noted that...

Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number.  For example √-9 isn't a real number as there is no

Matrices, Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+...

Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+6x2+x3-2x4-4x5=-1 3x1-9x2+8x3+4x4-13x5=49

Conjugate of the complex number, The conjugate of the complex number a + b ...

The conjugate of the complex number a + b i is the complex number a - b i .  In other terms, it is the original complex number along the sign on the imaginary part changed.  Here

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