Results 1 to 6 of 6
Like Tree3Thanks
  • 1 Post By SlipEternal
  • 1 Post By SlipEternal
  • 1 Post By hollywood

Math Help - Function points monotonic and increasing help?

  1. #1
    Member
    Joined
    Feb 2014
    From
    USA
    Posts
    231

    Function points monotonic and increasing help?

    Can anyone take a look at this question: Function points monotonic and increasing help?-capture11.jpgand tell me if my answer is correct? If not why not? I've already gotten some help with derivatives and second derivatives and how they behave compared to the original function, but I'm not sure about the "monotonic" meaning, I'm also not sure if the brackets change the outcome of option III. Any help? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: Function points monotonic and increasing help?

    Monotonic means if it increases, it does not also decrease. If it decreases, it does not also increase. Since it increases, it can be monotonic if and only if it does not decrease (which is true). The derivative can be approximated by taking the slope of the lines between adjacent points. Those slopes would be 1,2,3. So, it is possible that f'(x) is increasing. Next, II and III are saying the exact same thing. If II is true, then so is III (and vise versa). For III, you can only discount something if you have evidence to the contrary. Since you do not know if the function exists for x<-0.5 or x>-0.2, you cannot discount that it is possible. There is no evidence to the contrary, so it is possible.
    Thanks from canyouhelp
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2014
    From
    USA
    Posts
    231

    Re: Function points monotonic and increasing help?

    Quote Originally Posted by SlipEternal View Post
    Monotonic means if it increases, it does not also decrease. If it decreases, it does not also increase. Since it increases, it can be monotonic if and only if it does not decrease (which is true). The derivative can be approximated by taking the slope of the lines between adjacent points. Those slopes would be 1,2,3. So, it is possible that f'(x) is increasing. Next, II and III are saying the exact same thing. If II is true, then so is III (and vise versa). For III, you can only discount something if you have evidence to the contrary. Since you do not know if the function exists for x<-0.5 or x>-0.2, you cannot discount that it is possible. There is no evidence to the contrary, so it is possible.
    Okay, thank you. Would III just be decreasing though? Is it possible to know if it's concave up or just decreasing?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,845
    Thanks
    715

    Re: Function points monotonic and increasing help?

    Concave up means the derivative is increasing. Concave down means the derivative is decreasing.
    Thanks from canyouhelp
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Feb 2014
    From
    USA
    Posts
    231

    Re: Function points monotonic and increasing help?

    Quote Originally Posted by SlipEternal View Post
    Concave up means the derivative is increasing. Concave down means the derivative is decreasing.
    So aren't they all true then?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: Function points monotonic and increasing help?

    Yes, that's what SlipEternal said.

    - Hollywood
    Thanks from canyouhelp
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: September 21st 2013, 02:08 PM
  2. Family of monotonic strictly increasing functions...
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 24th 2012, 11:13 AM
  3. Replies: 2
    Last Post: October 29th 2009, 08:02 PM
  4. monotonic function
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 15th 2009, 10:21 AM
  5. Show that the function is monotonic
    Posted in the Calculus Forum
    Replies: 12
    Last Post: February 17th 2008, 01:53 PM

Search Tags


/mathhelpforum @mathhelpforum