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

8308 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve simultaneous equations: 3x + y = 12 and 5x + 5y = 30


Find the minimum value of the quadratic 3x^2-8x+1.


The perimeter of a right-angled triangle is 81 cm. The lengths of its sides are in the ratio 2 : 3 : 4. Work out the area of the triangle.


3/5 of a number is 162. Work out the number.


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