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

• Wessssss

## Homework Statement

Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root.

## 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"

Wessssss said:

## Homework Statement

Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root.

## 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?