I have a question regarding Intermediate Value theorem. I feel like I understand the concept but I'm

Nasir Kim

Nasir Kim

Answered question

2022-05-25

I have a question regarding Intermediate Value theorem. I feel like I understand the concept but I'm having trouble understanding a particular problem. I'm not what this problem is asking me to do, perhaps someone could clear it up for me. It reads as follows:
Show that if f is continuous on [0, 1] and 0 f ( x ) 1 for all x on [0, 1], then there exists at least one point c in [0, 1] at which f(c) = c. HINT: Apply the Intermediate Value theorem to the function g ( x ) = x f ( x ).
Obviously the last part is important, but I don't know how it all fits. This seems fairly different than proving that there lies a root of a function between two points.

Answer & Explanation

Krish Finley

Krish Finley

Beginner2022-05-26Added 14 answers

You want to prove that g ( x ) = 0 for some x. Can you apply the intermediate value theorem? Which interval would you choose?

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?