Results 1 to 5 of 5

Math Help - Need Help drawing a continuous function that satifies all conditions

  1. #1
    Member
    Joined
    Jul 2010
    Posts
    86

    Need Help drawing a continuous function that satifies all conditions

    I need help to see if my diagram i made at home is correct. I wrote my observations and if someone can include a diagram it would be greatly appriciated

    Sketch the graph of a continuos function that satisfies all of the following conditions:
    f'(x)>0 if /x/ <2 {/x/= absolute value of x}
    f'(x)<0 if /x/ >2
    f'(2)=0
    lim as x approaches positive infinity f(x)=2
    f(-x)=-f(x)
    f''(x) if 0<x<3
    f''(x)>0 if x>3

    soo i got the following
    - increasing from (-2,2)
    -decreasing from (-infinity,-2)
    -hoizontal tanget at x=2
    -vertical asyp at x=2
    -odd function
    -concave down from (0,3)
    -concave up from(3, infinity)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    Those interpretations look good. The only thing I would add is that it is also decreasing for x values from 2 to infinity. Do you have a sketch? It shouldn't be too hard to put these pieces together.

    Good luck!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2010
    Posts
    86
    Quote Originally Posted by apcalculus View Post
    Those interpretations look good. The only thing I would add is that it is also decreasing for x values from 2 to infinity. Do you have a sketch? It shouldn't be too hard to put these pieces together.

    Good luck!
    How did u get that.. from (2,infinity)? And no i have it written in my note book but i dont have a scanner.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member apcalculus's Avatar
    Joined
    Apr 2009
    From
    Boston
    Posts
    293
    |x| > 2 means x < -2 or x > 2. I hope this helps.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jul 2010
    Posts
    86
    Quote Originally Posted by apcalculus View Post
    |x| > 2 means x < -2 or x > 2. I hope this helps.
    Oh ok i see it now Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. prove that every continuous function is separately continuous
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: November 23rd 2011, 04:57 AM
  2. Replies: 3
    Last Post: April 18th 2011, 09:19 AM
  3. Replies: 3
    Last Post: April 18th 2011, 08:24 AM
  4. Replies: 1
    Last Post: November 3rd 2008, 01:28 PM
  5. Replies: 5
    Last Post: October 19th 2008, 05:14 AM

/mathhelpforum @mathhelpforum