• Support PF! Buy your school textbooks, materials and every day products Here!

Intermediate Value Theorem and Rolle's Theorem to show root

  • Thread starter Wessssss
  • Start date
  • #1
3
0

Homework Statement


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


Homework Equations





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"

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,519
734

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?
 

Related Threads on Intermediate Value Theorem and Rolle's Theorem to show root

Replies
1
Views
2K
Replies
18
Views
904
Replies
2
Views
1K
  • Last Post
Replies
18
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
2
Replies
31
Views
5K
  • Last Post
Replies
2
Views
6K
  • Last Post
Replies
3
Views
3K
Top