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: Inequality Proof

  1. Aug 12, 2010 #1
    1. The problem statement, all variables and given/known data

    If f(x) = (x-1)^2 and g(x) = x+1, then g is greater than or equal to f on the set S = {real numbers x : x is between 0 and 3}.

    2. Relevant equations

    g is greater than or equal to f on the set S of real numbers iff for all s in S, g(s) is greater than f(s).

    3. The attempt at a solution

    Since we know x is an element of S, we know that x is between 0 and 3. That is, (x)(x-3) is less than or equal to 0. And here is where I get stuck.

    I have tons of scratch paper that doesn't really show anything, and my TA gave what he calls a "proof" of this, but he assumed f(x) is less than or equal to g(x), but doesn't realize that assuming what you are trying to prove is not a way to prove anything. I just don't know how to start this.
    Last edited: Aug 12, 2010
  2. jcsd
  3. Aug 12, 2010 #2


    Staff: Mentor

    Hopefully, you have sketched a graph of both functions. If so, you should see that the two curves intersect at (0, 1) and (3, 4).

    Look at the expression x + 1 - (x - 1)2. On any interval where this expression is positive, g(x) > f(x). On any interval where the expression is negative, g(x) < f(x). Note that I am not a priori assuming either function is larger than the other.
  4. Aug 12, 2010 #3
    For some reason I never thought to subtract f(x) from g(x). It is proved! Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook