- #1
macbowes
- 15
- 0
Homework Statement
Using IVT, show that [tex]3(\cos(\pi x)) - 3x + 1[/tex] exists on interval (0,1)
Homework Equations
None
The Attempt at a Solution
I think I got the right idea, but on my quiz (this was a question I just had on a quiz) I didn't know if I was finished or not.
So when using 0 on the interval (0,1), this is the equation:
[tex]3(\cos(\pi 0)) - 3(0) + 1[/tex] =
[tex]3(\cos(0)) - 3(0) + 1[/tex] =
[tex]3(1) + 1[/tex] =
3 + 1 = 4
Then I used 1 on the interval, which yielded this:
[tex]3(\cos(\pi 1)) - 3(1) + 1[/tex] =
[tex]3(\cos(\pi)) - 3 + 1[/tex] =
[tex]3(-1) - 3 + 1[/tex] =
[tex]-3 - 3 + 1[/tex] = -5
So I've resulted in -5 and 4, which is large than (0,1), so does that means it exists on that interval? I've got these answers, but I'm not really sure what I do with them. I ended up just writing "squeeze", but when I handed it in he tsk'd at it, so I don't think that's right, lol.
EDIT: I'm trying to fix my post as I made a blatant error that LC pointed out, but what I'm trying to delete (3(1) = 4, lol) keeps appearing in latex in my post even though it's not there when I click the edit button. Anyone know what's up?
Last edited: