Results 1 to 3 of 3

Math Help - Curve Sketching

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    16

    Intrepreting Curve Sketching Conditions

    Interpret each piece of information, so that you can be able to sketch the graph of a function f that satisfies the following conditions:

    .(a) f(0) = 0

    .(b) f''(x) > 0, . x \neq 0

    .(c) \mathop {\lim }\limits_{x \to 0^-} f'(x) = \infty

    .(c) \mathop {\lim }\limits_{x \to 0^+} f'(x) = -\infty

    .(d) \mathop {\lim }\limits_{x \to -\infty} f(x) = -\infty

    .(d) \mathop {\lim }\limits_{x \to \infty} f(x) = \infty


    .

    My interpretations are as follows:

    .(a) y-intersect at (0,0)

    .(b) Concave up for all values of x, except at x = 0 (possibly an asymptote there?)

    .(c) As you approach 0 from the left, the slope approaches infinity and so the function gets higher.

    .(c) As you approach 0 from the right, the slope approaches negative infinity and so the function gets lower.

    .(d) As you approach negative infinity (left), the function gets lower and lower,

    .(d) As you approach positive infinity (right), the function gets higher and higher.


    I'm not to sure about them though, and it seems like (b) and (c) are contradictory (if C is true, that would mean concave down to the right of 0)

    I would really appreciate a second opinion.


    [NOTE: I do not need help with the sketching part, just with interpreting the conditions that f must satisfy.]
    Last edited by Some_One; February 21st 2009 at 05:31 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by Some_One View Post
    Sketch the graph of a function f that satisfies the following conditions:

    .(a) f(0) = 0

    .(b) f''(x) > 0, . x \neq 0

    .(c) \mathop {\lim }\limits_{x \to 0^-} f'(x) = \infty

    .(c) \mathop {\lim }\limits_{x \to 0^+} f'(x) = -\infty

    .(d) \mathop {\lim }\limits_{x \to -\infty} f(x) = -\infty

    .(d) \mathop {\lim }\limits_{x \to \infty} f(x) = \infty

    Interpret each piece of information.

    .

    My interpretations are as follows:

    .(a) y-intersect at (0,0)

    .(b) Concave up for all values of x, except at x = 0 (possibly an asymptote there?)

    .(c) As you approach 0 from the left, the slope approaches infinity and so the function gets higher.

    .(c) As you approach 0 from the right, the slope approaches negative infinity and so the function gets lower.

    .(d) As you approach negative infinity (left), the function gets lower and lower,

    .(d) As you approach positive infinity (right), the function gets higher and higher.

    I'm not to sure about them though, and it seems like (b) and (c) are contradictory (if C is true, that would mean concave down to the right of 0)

    I would really appreciate a second opinion.
    If and only if the second condition at d is

    \mathop {\lim }\limits_{x \to \infty} f(x) = -\infty

    then the function could be:

    f(x)=-\sqrt{|x|}
    Attached Thumbnails Attached Thumbnails Curve Sketching-spitzbeinull.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    16
    Quote Originally Posted by earboth View Post
    If and only if the second condition at d is

    \mathop {\lim }\limits_{x \to \infty} f(x) = -\infty

    then the function could be:

    f(x)=-\sqrt{|x|}

    But it's not. For the assignment we can't change the given conditions. They are what they are - unless you can without a doubt say that they are contradictory, then I can dispute the question with my teacher.

    The main part of the assignment is to interpret the meaning of the conditions. Then we just have to roughly sketch the curve based on those four things.

    We do not have to find the equation of the function.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. curve sketching
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 8th 2010, 02:32 AM
  2. Curve Sketching
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 26th 2010, 07:20 PM
  3. Curve Sketching
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 3rd 2010, 02:48 AM
  4. Curve Sketching
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 19th 2009, 03:09 PM
  5. Curve Sketching again~
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 18th 2008, 02:55 PM

Search Tags


/mathhelpforum @mathhelpforum