1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Intermediate Value Theorem

  1. Apr 15, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant 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

    3. 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.
  2. jcsd
  3. Apr 15, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are looking for a root, that is where f(c) = 0. So it would be good if your interval had f(x) having opposite signs at the ends.
  4. Apr 15, 2013 #3

    I can't even remember roots. I guess I have to brush up on that.

    By the way, just telling me that with that ONE SENTENCE was more than anything that particular tutor could do. I appreciate your succinctness.


    Ok, so to solve this, I could choose [-1/2, 0] ?

    [-1/8, 1]

    Zero exists between those two points, its a continuous function, so f(c)= 0 exists. Look alright?
    Last edited: Apr 15, 2013
  5. Apr 15, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, but you could phrase it better: "f(-1/2)=-1/8 and f(0) = 1 so by the intermediate value theorem there exists a c between -1/8 and 1 such that f(c) = 0".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted