- #1

- 32

- 0

## Homework Statement

Use the IVT to find an interval of length 1/2 containing a root of

f(x)=x

^{3}+ 2x + 1

## Homework Equations

**Intermediate Value Theorem:**If f(x) is continuous on a closed interval [a, b] and f(a)≠f(b) then for every value M between f(a) and f(b) there exists at least one value c[itex]\in[/itex](a, b) such that f(c) = M

## The Attempt at a Solution

So I am thinking with this what I need to do is take any 1/2 length interval and plug in those values for x. I took [0, 1/2] and plugged it in. I got

f(0) = 1

f(1/2) = 2.125 or 2 1/8. It just asked to find an interval. So I would think I could say f(c) exists somewhere between f(0) and f(1/2) because they are both continuous functions.

Let me know if this is right, because the math tutor told me it was wrong, and I think he's wrong.