Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By SlipEternal

Math Help - the sign of the first derivative

  1. #1
    Senior Member
    Joined
    Sep 2013
    From
    Portland
    Posts
    480
    Thanks
    70

    the sign of the first derivative

    Maybe this is a question that is a bit redundant.

    I just started the chapter on curve sketching. The first section is about local maxima and minima.

    How do I determine the sign of the first derivative to see if it changes at the possible turning point? I know that a function like f(x) = x^3 doesn't have a turning point.

    Do I need to start sketching the curve by plotting the possible turning points or is there a more intuitive way to determine if there is a sign change.

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,880
    Thanks
    742

    Re: the sign of the first derivative

    The derivative of a function has the intermediate value property. Find all values of x where the derivative is zero or where it does not exist. Suppose you find the values \{a_1,\ldots,a_n\} where the derivative is zero or it does not exist. Then consider the intervals: (-\infty,a_1), (a_1,a_2), \ldots, (a_{n-1},a_n), (a_n,\infty). For each interval, if the derivative is positive, it is positive for every value of the interval. If it is negative, it is negative for every value of the interval. So, just pick any point in the interval and plug it into the derivative. That will tell you the sign of the derivative on the entire interval.
    Thanks from Jonroberts74
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Sep 2013
    From
    Portland
    Posts
    480
    Thanks
    70

    Re: the sign of the first derivative

    Thank you!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: October 17th 2012, 08:55 PM
  2. [SOLVED] Where does the sign go?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 9th 2011, 06:28 AM
  3. sign
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 2nd 2009, 10:53 PM
  4. What does this sign mean?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 19th 2009, 08:10 AM
  5. Sign Charts
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 19th 2009, 10:43 AM

Search Tags


/mathhelpforum @mathhelpforum