Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By MarkFL

Math Help - Extremas

  1. #1
    Junior Member Greymalkin's Avatar
    Joined
    Jun 2012
    From
    Montreal
    Posts
    74
    Thanks
    1

    Extremas

    Find extrema (x^2-8)^{2/3}
    Answers are \pm 2\sqrt{2} and 0 for x values,
    Local minimas are (\pm 2\sqrt{2},0)
    Which makes complete sense if you look at the graph, however algebraically I solve for local maxima (0,4) which makes no sense to me as its undefined on the graph, why does my book say it counts as a local maxima if its "undefined"?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Extremas

    We are given:

    f(x)=(x^2-8)^{\frac{2}{3}}

    and we find:

    f'(x)=\frac{2}{3}(x^2-8)^{-\frac{1}{3}}(2x)=\frac{4x}{3(x^2-8)^{\frac{1}{3}}}

    So, we see we have the 3 critical values:

    x=-2\sqrt{2},0,2\sqrt{2}

    While the derivative is undefined for x=\pm2\sqrt{2}, the function is defined there, indicating we have cusps at these points.

    We then find on the intervals:

    (-\infty,-2\sqrt{2}) derivative is negative, function is decreasing.

    (-2\sqrt{2},0) derivative is positive, function is increasing.

    (0,2\sqrt{2}) derivative is negative, function is decreasing.

    (2\sqrt{2},\infty) derivative is positive, function is increasing.

    So, by the first derivative test for extrema, we find minima at:

    (\pm\sqrt{2},0)

    and a maximum at (0,4).
    Thanks from Greymalkin
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quick question on extremas
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 15th 2009, 04:51 AM
  2. Questions about relative extremas?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 25th 2008, 08:51 PM
  3. Critical Numbers & Extremas
    Posted in the Calculus Forum
    Replies: 10
    Last Post: November 9th 2008, 03:36 PM
  4. Global Extremas
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 4th 2007, 02:11 PM

Search Tags


/mathhelpforum @mathhelpforum