Results 1 to 2 of 2

Math Help - asymptotes

  1. #1
    Banned
    Joined
    Aug 2007
    Posts
    52

    asymptotes

    A family of functions is given by

    Find values of a and b so that the function r has a local minimum at the point (5 , 9)

    Find the vertical asymptotes of r with the values of a and b found in part (a).


    ok can someone just help me start this one...it would help alot, thanks

    mer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by mer1988 View Post
    A family of functions is given by

    Find values of a and b so that the function r has a local minimum at the point (5 , 9)

    Find the vertical asymptotes of r with the values of a and b found in part (a).


    ok can someone just help me start this one...it would help alot, thanks

    mer
    Hello,

    1. I can't open the files which probably show what you have done so far

    2. Calculate the derivative. Use chain rule:

    r'(x) = (-1)(a-(x-b)^2)^{-2}) \cdot 2(x-b) = -\frac{2(x-b)}{\left(a-(x-b)^2\right)^{2}}

    3. You already know that r'(5) = 0. A fraction equals zero if the numerator is zero (and the denominator is not zero, of course):

    2(5-b) = 0~\iff~b = 5

    4. You already know that the point M(5, 9) is placed on the graph of the function:

    r(x) = \frac{1}{a-(x-5)^2}~\implies~r(5) = \frac{1}{a-(5-5)^2}=\frac1a=9~\implies~a=\frac19

    Thus the equation of the function is: r(x) = \frac{1}{\frac19 - (x-5)^2}

    5. To find the vertical asymptotes you have to calculate the zeros of the denominator:

    \frac19-(x-5)^2=0 Solve for x. I've got x=\frac{14}{3}~\vee~x=\frac{16}{3}

    6. I've attached a diagram of the function.
    Attached Thumbnails Attached Thumbnails asymptotes-zwei_vert_asympt.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Asymptotes
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 27th 2009, 07:30 PM
  2. asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 8th 2009, 04:16 PM
  3. Help with asymptotes
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 4th 2009, 05:54 PM
  4. asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 27th 2007, 05:33 PM
  5. asymptotes
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 22nd 2007, 04:07 AM

Search Tags


/mathhelpforum @mathhelpforum