Use the intermediate value theorem to show that there is a root of the given equation in the specified interval. root(3)(x)=1-x,(0,1) Intermediate Value Theorem: Suppose that f is continuous on the closed interval[a,b] and let N be any number betweenf(a) and f(b), where f(a)ne f(b). Then there exists a number c in (a,b) such that f(c) = N.

Yair Valentine

Yair Valentine

Answered question

2022-08-04

Use the intermediate value theorem to show that there is a root of the given equation in the specified interval. x 3 = 1 x , ( 0 , 1 )
Intermediate Value Theorem:
Suppose that f is continuous on the closed interval [a,b] and let N be any number betweenf(a) and f(b), where f ( a ) f ( b ).
Then there exists anumber c in (a,b) such that f(c) = N.

Answer & Explanation

Holly Crane

Holly Crane

Beginner2022-08-05Added 14 answers

f ( x ) = x = ( 1 x ) 3 , ( 0 , 1 )
= 1 x 3 3 x + 3 x 2
Formula: If 'f' is a continuous function,then
Intermediatemean value theorem f ( c ) = f ( b ) f ( a ) b a , a b , c [ a , b ]
f ( c ) = f ( 1 ) f ( 0 ) 1 0 , c [ 0 , 1 ]
= 0 1 1 0
=-1
This is true for f(c)=n, where for all n N f ( c ) = n.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?