Use the IVT to find an interval of length 1/2 containing a root of
f(x)=x3+ 2x + 1
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.