Results 1 to 6 of 6

Math Help - Analyze the function for local extreme points, concavity and inflection points

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    23

    Analyze the function for local extreme points, concavity and inflection points

    f(x) = 2x^2+2x+3

    Ok, so I know the function is increasing because f^1(x)=4x+2 which is positive
    also it is concave up because f^{11}=4 which is also positive

    Please teach me how to solve for local extreme points and inflection points, and for concavity, do I just answer concave up?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jkami View Post
    f(x) = 2x^2+2x+3

    Ok, so I know the function is increasing because f^1(x)=4x+2 which is positive Mr F wonders: Is it positive for all values of x ....?

    also it is concave up because f^{11}=4 which is also positive Mr F says: What is the definition given for concave up in your class notes?

    Please teach me how to solve for local extreme points Mr F says: What do your class notes tell you to do?

    and inflection points, and for concavity, do I just answer concave up?
    ..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    23
    Derivative
    If postive, then function increasing
    If negative, then function decreasing
    If zero, then critical point

    Second Derivative
    If positive, then concave up
    If negative, then concave down
    If zero, then inflection point

    So I figured the minimum point is (- \frac 1{2}, \frac 5{2}), so what is the inflection point
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jkami View Post
    Derivative
    If postive, then function increasing
    If negative, then function decreasing
    If zero, then critical point

    Second Derivative
    If positive, then concave up
    If negative, then concave down
    If zero, then inflection point

    So I figured the minimum point is (- \frac 1{2}, \frac 5{2}), so what is the inflection point
    OK. So where exactly are you stuck in the questions you posted?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2009
    Posts
    23
    The problem asked for 3 things

    1. extreme points
    2. concavity
    3. inflection points

    I figured

    1. extreme point = (-\frac1{2},\frac5{2}) at minimum

    2. concavity = concave up

    Now I still need the inflection point

    I noticed that f^{11}(x) = 4, so does it mean there are no inflection points?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jkami View Post
    [snip]
    Now I still need the inflection point

    I noticed that f^{11}(x) = 4, so does it mean there are no inflection points?
    Yes, that's what it means.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Concavity & Points of Inflection
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 23rd 2010, 03:46 AM
  2. Replies: 2
    Last Post: March 26th 2010, 08:36 AM
  3. concavity and inflection points
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 30th 2009, 02:47 PM
  4. Points of inflection and concavity
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 27th 2009, 02:48 PM
  5. Replies: 1
    Last Post: September 16th 2007, 03:53 PM

Search Tags


/mathhelpforum @mathhelpforum