Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - Increasing function interval

  1. #1
    Junior Member BERMES39's Avatar
    Joined
    Aug 2011
    Posts
    41

    Increasing function interval

    For a function such as f(x) = -x^2 +2x +2, a parabola with a maximum at (1,3) a textbook says that the function is increasing in the interval (-infinity, 1]. If this is correct could someone tell me why? I think at x = 1 the slope is 0, so the function is not increasing and the interval should be: (-infinity, 1). Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: Increasing function interval

    Quote Originally Posted by BERMES39 View Post
    For a function such as f(x) = -x^2 +2x +2, a parabola with a maximum at (1,3) a textbook says that the function is increasing in the interval (-infinity, 1]. If this is correct could someone tell me why? I think at x = 1 the slope is 0, so the function is not increasing and the interval should be: (-infinity, 1). Thanks.
    Increasing/Decreasing Test Theorem
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,952
    Thanks
    1629

    Re: Increasing function interval

    If you look at just the interval (-\infty, 1], you see that for x in that interval but not equal to 1, f(x)< f(1) so f is "increasing at x= 1". Of course, if you use an interval on both sides of x= 1, that is not true.

    Of course you could also say "f is decreasing on [1, \infty)" so it seems that we are saying f is both increasing and decreasing at x= 1. However, the point is that we are looking at the two intervals separately.
    Last edited by HallsofIvy; March 13th 2012 at 05:08 PM.
    Thanks from BERMES39
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 18th 2009, 03:35 PM
  2. Replies: 1
    Last Post: November 28th 2008, 08:16 AM
  3. Replies: 4
    Last Post: November 14th 2008, 03:48 PM
  4. Replies: 3
    Last Post: March 13th 2008, 07:26 AM
  5. Increasing interval and decreasing interval
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 24th 2006, 08:49 AM

Search Tags


/mathhelpforum @mathhelpforum