Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By StefanTM
  • 1 Post By Soroban

Math Help - #Times f(x)=0

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Europe
    Posts
    12

    #Times f(x)=0

    f(x) = x4-4x3-8x2+4

    How many times does f(x) = 0? (excuse the bad formulation)

    Hint: Gather as much information from the derivative of f(x) as possible. We are only interested in the number of times f(x) equals zero.

    Okay so differentiating the function is simple: f ' (x) = 4x3-12x2-16x, but what kind of information do I need to extract in order to determine how many times f(x)=0?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2012
    From
    Germany
    Posts
    27
    Thanks
    4

    Re: #Times f(x)=0

    Hi Cinnaman,
    a few tipps:
    f'(x)=0 => x1=-1, x2= 0; x3=4 the event. max- and min points of f(x)
    If f''(x1) < 0 => x1 is max. point =>MAX1( x1|f(x1))
    If f''(x1) > 0 => x1 is min. point =>MIN1( x1|f(x1))
    analog with x2 und x3.
    EXTx= Extrem x-point;
    xp<xn;
    If sign of f(EXTxp) is not = f(EXTxn) => there is a x, beetwen xp und xn with f(x)=0
    Thanks from Cinnaman
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Europe
    Posts
    12

    Re: #Times f(x)=0

    Ah, that makes sense, thank you.

    I figured out that there is no x where f(x)=0 between x=-1 and x=0, but there is one between x=0 and x=4.

    Is the last step now to take the limit as x approaches inf / -inf and use them as extreme points aswell?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    691

    Re: #Times f(x)=0

    Hello, Cinnaman!

    f(x) \:= \:x^4 - 4x^3 - 8x^2 + 4

    How many times does f(x) = 0 ?

    Hint: Gather as much information from the derivative of f(x) as possible.
    We are only interested in the number of times f(x) equals zero.

    Set f'(x) = 0 and solve.

    . . 4x^3 - 12x^2 - 16x \:=\:0 \quad\Rightarrow\quad 4x(x+1)(x-4) \:=\:0 \quad\Rightarrow\quad x \:=\:\text{-}1,0,4


    There are horizontal tangents at: (\text{-}1,1),\:(0,4),\:(4,\text{-}124)


    The Second Derivative Test give us: . \begin{Bmatrix}(\text{-}1,1) & \text{min.} \\ (0,4) & \text{max.} \\ (4,\text{-}124) & \text{min.} \end{Bmatrix}

    The graph looks like this.
    Code:
                   |
          *        |
                  -*-
           *     * | *          *
            *   *  |  *
             -*-   |
      -------------+---♥-------♥---
                   |
                   |    *     *
                   |     *   *
                   |      -*-
                   |
    Therefore, the graph crosses the x-axis twice.
    Thanks from Cinnaman
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Flip a weighted coin n times, flip again another n times
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 4th 2012, 01:34 PM
  2. I tried doing this 3 times already!!!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 27th 2012, 07:19 PM
  3. [SOLVED] |a\times b| = LCM[|a|, |b|]
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 9th 2011, 10:35 PM
  4. Replies: 1
    Last Post: February 7th 2010, 12:18 AM
  5. Replies: 2
    Last Post: December 9th 2007, 02:33 PM

Search Tags


/mathhelpforum @mathhelpforum