Results 1 to 5 of 5

Math Help - multiple choice on stationary points

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    7

    multiple choice on stationary points

    x^3 -6x^2 +12x +18
    Which one of these choices are correct( Choose A,B,C OR D only)
    A. X=2 is a point of inflection
    B. X=2 is an upward turning point and x=0 is a downward turning point
    C. X=2 is a downward turning point and x=0 is a upward turning point
    D. X=2 can not be characterised because f(x)=0

    The graph are below: Showing the point at X=2


    Uploaded with ImageShack.us

    Thanks a lot for answering the question.
    Last edited by CaptainBlack; November 4th 2010 at 02:32 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Quote Originally Posted by firebrend View Post
    x^3 -6x^2 +12x +18
    Which one of these choices are correct( Choose A,B,C OR D only)
    A. X=2 is a point of inflection
    B. X=2 is an upward turning point and x=0 is a downward turning point
    C. X=2 is a downward turning point and x=0 is a upward turning point
    D. X=2 can not be characterised because f(x)=0

    The graph are below: Showing the point at X=2


    Uploaded with ImageShack.us
    what is your answer, and why?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    7
    my answer is A, because at x=2 f'(x)=0 and f''(x)=0==> the point is stationary point but is neither maximum nor minimum point. therefore it is an inflection point. What about your answer? do you agree with my reasoning? thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Quote Originally Posted by firebrend View Post
    my answer is A, because at x=2 f'(x)=0 and f''(x)=0==> the point is stationary point but is neither maximum nor minimum point. therefore it is an inflection point. What about your answer? do you agree with my reasoning? thanks
    I agree, to a point.

    I still believe that it is necessary to show that f''(x) changes sign at x = 2 to confirm a point of inflection.

    I can't say for sure that there is not some function that exists where f'(a) = 0, f''(a) = 0 , has no extrema at (a,f(a)) , and that does not have an inflection point at x = a ... I just can't think of a rigorous proof of your statement or a suitable counterexample.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,697
    Thanks
    1469
    If f(x)= x^3 -6x^2 +12x +18 then f'(x)= 3x^2- 12x+ 12= 3(x^2- 4x+ 3)= 3(x- 3)(x- 1) which is ot 0 at x= 2 so 2 is not a critical point and is not 0 at x= 0 so 0 is not a turning point. f''(x)= 6x- 12= 6(x- 2). Yes, f''(2)= 0 and f''(x) changes sign at x= 2 (f''(x) is negative for x< 2, positive for x> 2).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 24th 2011, 11:35 AM
  2. Multiple Choice Help
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: September 13th 2009, 08:57 PM
  3. Multiple Choice
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 27th 2009, 03:38 AM
  4. Multiple choice
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: February 23rd 2008, 08:37 PM
  5. Multiple choice
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 23rd 2008, 06:14 PM

Search Tags


/mathhelpforum @mathhelpforum