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.

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I have a question regarding Intermediate Value theorem. I feel like I understand the concept but I&#039;m having trouble understanding a particular problem. I&#039;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&#039;t know how it all fits. This seems fairly different than proving that there lies a root of a function between two points.

Krish Finley · Accepted Answer

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

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

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