Results 1 to 4 of 4

Math Help - absolute minimum value

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    49

    absolute minimum value

    show that the function f(x) = e^x-x-1 has an absolute value and deduce that
    e^x>= x+1 for all x inside R.

    for the first part of the question, i tried

    f'(x)= e^x -1 = 0 => x = ln1 = 0 ==> x=0, y=0

    but how we know that it is an absolute min since the range of the function is not given??? then how to solve the second part of the question??? plz help me...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    If you know how to derive you can calculate f'(x) and find the variations of f and show that f has a minimum for x=0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    49
    Quote Originally Posted by running-gag View Post
    Hi

    If you know how to derive you can calculate f'(x) and find the variations of f and show that f has a minimum for x=0
    how to do so??? still blurrr....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    f(x) = e^x-x-1

    f'(x) = e^x-1
    is negative for x < 0 and positive for x > 0

    f is decreasing up to 0 and increasing from 0, therefore has a minimum for x=0 which is f(0)=0

    for all x
    f(x) > f(0)
    e^x > x+1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: May 23rd 2010, 10:59 PM
  2. absolute maximum and absolute minimum value
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 18th 2009, 03:25 PM
  3. finding absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 15th 2009, 04:22 PM
  4. Replies: 2
    Last Post: November 8th 2009, 01:52 PM
  5. Find the absolute maximum and absolute minimum
    Posted in the Calculus Forum
    Replies: 5
    Last Post: December 12th 2008, 09:46 AM

Search Tags


/mathhelpforum @mathhelpforum