Results 1 to 2 of 2

Math Help - Taylor Expansion

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    9

    Taylor Expansion

    Rather stuck on the following:

    The function f(x) has Taylor expansion a0 + a1x + a2x^2 + ... around x=0.
    If a1 = 0, and a2>0 explain why f >= (greater than, OR equal to) a0 near x=0

    First of all, am i right in saying this can also be called a Maclaurin series, since we're considering it around x = 0?

    And, secondly...well, not really sure where to begin, or how to phrase my answer, I can see why it would be true from the info given..but having difficulty putting it into the correct form...

    If anyone can help, it would be greatly appreciated.
    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 scorpio1 View Post
    Rather stuck on the following:

    The function f(x) has Taylor expansion a0 + a1x + a2x^2 + ... around x=0.
    If a1 = 0, and a2>0 explain why f >= (greater than, OR equal to) a0 near x=0

    First of all, am i right in saying this can also be called a Maclaurin series, since we're considering it around x = 0?

    And, secondly...well, not really sure where to begin, or how to phrase my answer, I can see why it would be true from the info given..but having difficulty putting it into the correct form...

    If anyone can help, it would be greatly appreciated.
    f'(0)=0, so 0 is a stationary point of f, f''(0)>0 so 0 is a local minima
    of f, so for x close enough to 0, f(x)>f(0).

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylor expansion?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 27th 2010, 05:15 AM
  2. Taylor Expansion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 9th 2009, 05:44 AM
  3. Taylor Expansion?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 31st 2009, 03:12 PM
  4. Taylor Expansion x^2+y^2+z^2=9
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 28th 2009, 05:26 PM
  5. Taylor Expansion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 27th 2009, 11:56 PM

Search Tags


/mathhelpforum @mathhelpforum