Results 1 to 5 of 5

Math Help - Identifying any cusp or vertical tangents

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    8

    Wink Identifying any cusp or vertical tangents

    I am not sure how to identify any cusp or vertical tangents. I can find the coordinates of the local extrema using the interval charts, though.

    Can somebody help me with these following question:

    Q. Determine the ecoordinates of the local extrema. Identify any cusps or vertical tangents.
    a) y=-t^(2)e^(3t)
    b) y= (x-5)^(1/3)
    c) f(x)=(x^(2)-1)^(1/3)
    Last edited by dkssudgktpdy; June 6th 2010 at 06:05 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    244
    Quote Originally Posted by dkssudgktpdy View Post
    I am not sure how to identify any cusp or vertical tangents. I can find the coordinates of the local extrema using the interval charts, though.

    Can somebody help me with these following question:

    Q. Determine the ecoordinates of the local extrema. Identify any cusps or vertical tangents.
    a) y=-t^(2)e^(3t)
    b) y= (x-5)^(1/3)
    c) f(x)=(x^(2)-1)^(1/3)
    Minima and maxima occur when the derivative is zero, also vertical tangeants when the derivative doesn't exist. (I think I remembered that last part right)

    so dy/dt = 2t*e^{3t} + t^2 3e^{3t}; solving for zero gives t=-2/3. I think t=0 is also an extrema point but I'll leave that to you to check out. Also check your answer using a graphing calculator or software such as MATLAB. If you need further help, please ask and I'll detail the answer further.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    8
    Quote Originally Posted by oldguynewstudent View Post
    Minima and maxima occur when the derivative is zero, also vertical tangeants when the derivative doesn't exist. (I think I remembered that last part right)

    so dy/dt = 2t*e^{3t} + t^2 3e^{3t}; solving for zero gives t=-2/3. I think t=0 is also an extrema point but I'll leave that to you to check out. Also check your answer using a graphing calculator or software such as MATLAB. If you need further help, please ask and I'll detail the answer further.

    So.. If I have both local maxima and local minima, there are no vertical tangents or cusps?

    I got the derivative part, but I am just not sure about identifying vetical tangents and cusps...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2010
    Posts
    107
    Quote Originally Posted by dkssudgktpdy View Post
    So.. If I have both local maxima and local minima, there are no vertical tangents or cusps?

    I got the derivative part, but I am just not sure about identifying vetical tangents and cusps...
    To determine any cusps/vertical tangets/corners, take the derivative of the function, and see if there is any point that will make the derivative undefined.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jun 2010
    Posts
    8
    Quote Originally Posted by lilaziz1 View Post
    To determine any cusps/vertical tangets/corners, take the derivative of the function, and see if there is any point that will make the derivative undefined.

    Ok.. so it means the first question that I wrote does not have both vertical tangent and cusp, right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. angle of inner tangents with the vertical
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 19th 2010, 05:46 AM
  2. Replies: 0
    Last Post: October 5th 2009, 10:49 PM
  3. Vertical tangent or cusp
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 20th 2009, 06:01 PM
  4. Replies: 1
    Last Post: May 30th 2009, 03:59 PM
  5. Horizontal and Vertical Tangents!
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 11th 2007, 08:20 AM

Search Tags


/mathhelpforum @mathhelpforum