Results 1 to 4 of 4

Math Help - graph defined?

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    57

    graph defined?

    Hi,

    I am attempting to graph (x^2-3)^\frac{2}{3}.

    My textbook shows the graph as being defined between \sqrt{3} and -\sqrt{3} in fact the derivative indicates that the graph has a local maximum at x=0. In my textbook the graph is convex and positive between \pm\sqrt{3}

    The problem is that f(0)=-3^\frac{2}{3} is approximately -2.08. Which means it's negative, unless I am calculating f(0) incorrectly? What has me really confused is that MuPAD does not show the graph as defined between \sqrt{3} and -\sqrt{3} which has got me thinking the textbook might be wrong. When calculating -3^\frac{2}{3} do you square the minus three and then take a cube root? Maybe that's what's wrong. Maybe f(0) is actually positive?

    Regards
    Craig.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2006
    Posts
    77
    Re-writing f as

    (\sqrt[3]{x^2-3})^2 should hopefully convince you that for real x this is always positive.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    57

    Calculators don't work...

    Hi,

    Thanks, looking at my notes that what I originally thought.
    Does that mean that f(0)=(-3)^\frac{2}{3} is approximately positive 2.08? My calculator gives (\sqrt[3]{3}[\frac{1+i\sqrt{3}}{2}])^2 which blows my pip. Why all the complex numbers if it's 2.08?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Sep 2006
    Posts
    77
    Cube rooting is defined all along the real line; no complex numbers should be involved at all. Yes f(0) is approximately +2.08.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: January 17th 2011, 01:46 AM
  2. Well defined
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: June 26th 2010, 02:39 PM
  3. Which of the following is not defined?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 12th 2009, 02:23 PM
  4. Replies: 2
    Last Post: August 5th 2009, 10:20 AM
  5. well defined
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 22nd 2008, 01:06 PM

Search Tags


/mathhelpforum @mathhelpforum