Results 1 to 2 of 2

Math Help - Advance Calculus Problem

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Advance Calculus Problem

    Q: Let f:[0,inf) -> R satisfy f(0) = 1 and f(x) >= x^2 for all x in [0,inf). Suppose that f is continuous on [0,inf). For which real numbers, c, can we say that the equation f(x) = c must have a solution?

    To be honest, I don't even know how to start this problem, all I know is something to do with the intermediate value theorem.

    Thank you!

    KK
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by tttcomrader View Post
    Q: Let f:[0,inf) -> R satisfy f(0) = 1 and f(x) >= x^2 for all x in [0,inf). Suppose that f is continuous on [0,inf). For which real numbers, c, can we say that the equation f(x) = c must have a solution?

    To be honest, I don't even know how to start this problem, all I know is something to do with the intermediate value theorem.

    Thank you!

    KK
    It looks to me that c must be >=1, for f(x)=c to have a root.

    This is because we are guaranteed that f(0)<=c and there is some u, such that f(u)>c, then the intermediate value theorem tells us that there is a root of f(x)=c in [0,u).

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with an integral. Thanks in advance!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 3rd 2010, 08:33 PM
  2. Paying In Advance
    Posted in the Business Math Forum
    Replies: 2
    Last Post: October 16th 2009, 11:50 AM
  3. advance calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2008, 12:45 AM
  4. Advance functions
    Posted in the Algebra Forum
    Replies: 0
    Last Post: November 11th 2008, 09:26 AM
  5. Discrete!! Please Help. thanks in advance
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 25th 2008, 10:23 AM

Search Tags


/mathhelpforum @mathhelpforum