Results 1 to 3 of 3

Math Help - Minimum value of function

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    6

    Minimum value of function

    Hi,
    I need to tell what's the minimum value of this function:

    f(x)=\sqrt{x+2(1+ \sqrt{x+1})} + \sqrt{x+2(1-\sqrt{x+1})}

    It's probably 2, but I have no idea how to prove it.
    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by bobb12 View Post
    Hi,
    I need to tell what's the minimum value of this function:

    f(x)=\sqrt{x+2(1+ \sqrt{x+1})} + \sqrt{x+2(1-\sqrt{x+1})}

    It's probably 2, but I have no idea how to prove it.
    Thanks in advance
    Here are the steps to solve this problem:

    First find the domain of the function.

    work NOT shown it is [0,\infty)

    So the domain has one boundary point.

    2nd find the derivative and set it equal to zero. (there are no solutions,again work not shown)

    So the global minimum must occur at the boundary point. x=0

    and f(0)=2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2011
    Posts
    6
    Quote Originally Posted by TheEmptySet View Post
    Here are the steps to solve this problem:

    First find the domain of the function.

    work NOT shown it is [0,\infty)

    So the domain has one boundary point.

    2nd find the derivative and set it equal to zero. (there are no solutions,again work not shown)

    So the global minimum must occur at the boundary point. x=0

    and f(0)=2
    Thanks a lot, but could You tell me how i can find the derivative of this function?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Minimum value for the function:
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 5th 2010, 06:55 PM
  2. how to prove a function has a minimum
    Posted in the Calculus Forum
    Replies: 0
    Last Post: July 18th 2010, 04:34 PM
  3. Writing out the minimum function
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 23rd 2010, 03:30 AM
  4. Minimum Value of Function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 7th 2008, 10:52 AM
  5. The minimum of the function
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 3rd 2007, 05:16 AM

Search Tags


/mathhelpforum @mathhelpforum