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Intermediate Value Theorem and Rolle's Theorem to show root

by Wessssss
Tags: intermediate, rolle, root, theorem
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Wessssss
#1
Oct27-11, 12:23 PM
P: 3
1. The problem statement, all variables and given/known data
Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root.


2. Relevant equations



3. The attempt at a solution
I'm not really sure what the question is asking for. the theorems I believe are to prove the existence of a point between a closed interval, but I have no interval, and what does it mean by "one root"
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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LCKurtz
#2
Oct27-11, 12:37 PM
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Quote Quote by Wessssss View Post
1. The problem statement, all variables and given/known data
Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root.

3. The attempt at a solution
I'm not really sure what the question is asking for. the theorems I believe are to prove the existence of a point between a closed interval, but I have no interval, and what does it mean by "one root"
Hint: Check f(0) and f(pi). And "one root" means the graph touches the x axis only once. And if you find one root, what can you conclude from Rolle's theorem if you have another root?


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