## Intermediate Value Theorem and Rolle's Theorem to show root

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

Recognitions:
Gold Member
Homework Help
 Quote by Wessssss 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?