Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity). Using the Intermidiate Value Theorem, it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3. Therefore, 

f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3] and taking N=2, we can therefore guarantee the existance of a number c such that 0<c<2 and c^2 = 2. 

DK
Answered by Dilyana K. Maths tutor

8498 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

there are 11 sweets in a box four are soft centred and seven hard centred sweets two sweets are selected at random a)calculate the probability that both sweets are hard centred, b) one sweet is soft centred and one sweet is hard centred


x^2+10x+6=0 Find x


The first four terms in a sequence are: -1, -4, -7, -10. Write an expression for the nth term of the sequence.


Factorise x^2-x-12


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences