Results 1 to 10 of 10
Like Tree1Thanks
  • 1 Post By hollywood

Math Help - finding maximum and minimum points of a two variable function

  1. #1
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    finding maximum and minimum points of a two variable function

    Here's the function
    x^2 + 4y^2 - 2x - 16y + 13 = 0

    Now time to take the derivative with respect to x, I got
    fx = 2x + 0 - 2 - 0
    = 2x - 2
    Now time to take the derivative with respect to y, I got
    fy = 0 + 8y - 0 - 16
    = 8y - 16

    This is what I got so far and Idk wether I did it right.... is there anything i did wrong?
    Last edited by asilvester635; November 17th 2012 at 01:28 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Dark Sun's Avatar
    Joined
    Apr 2009
    From
    San Francisco, California
    Posts
    36
    Thanks
    1

    Re: finding maximum and minimum points of a two variable function

    What was the question asking for exactly?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: finding maximum and minimum points of a two variable function

    The book is asking to find the maximum and minimum points on the graph.... (Finding maximum and minimum points with two variable functions)
    Here's how it looks like on the book
    finding maximum and minimum points of a two variable function-screen-shot-2012-11-17-2.23.13-pm.png
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,408
    Thanks
    1294

    Re: finding maximum and minimum points of a two variable function

    The critical points are located where both of the partial derivatives are 0.

    Then you need to check their nature using the Hessian.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: finding maximum and minimum points of a two variable function

    sorry i don't understand the equation..... although i have the work that I've done so far posted up there.... can you please check if i did it right?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: finding maximum and minimum points of a two variable function

    PLEASE ANYONE???!!!!!! im very confused.. ((
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: finding maximum and minimum points of a two variable function

    ProveIt: I think the OP meant to implicitly define a graph in the x-y plane, not a function of two variables.

    asilvester635: You have \frac{dy}{dx}=\frac{\partial{f}/\partial{x}}{\partial{f}/\partial{y}}, so the minimum and maximum y values are going to occur when \frac{\partial{f}}{\partial{x}}=0. This is when x=1, and plugging in to the equation gives:
    x^2+4y^2-2x-16y+13=0
    1+4y^2-2-16y+13=0
    4y^2-16y+12=0
    y^2-4y+3=0
    y=1,3
    So (1,1) is a minimum and (1,3) is a maximum.

    As it turns out, there is a more geometric way to analyze this function. Complete the square in both x and y:
    x^2+4y^2-2x-16y+13=0
    x^2-2x+4y^2-16y=-13
    x^2-2x+1+4y^2-16y+16=-13+1+16=4
    (x-1)^2+4(y-2)^2=4
    so the graph is an ellipse centered at (1,2), and the minimum and maximum points are (1,1) and (1,3) as before.

    - Hollywood
    Thanks from asilvester635
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: finding maximum and minimum points of a two variable function

    so minimum is (1,1) and maximum is (1,3)????
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: finding maximum and minimum points of a two variable function

    oops sorry i didn't read the whole thing lol...
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: finding maximum and minimum points of a two variable function

    No problem.

    - Hollywood
    Last edited by hollywood; November 17th 2012 at 09:27 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 12
    Last Post: May 20th 2011, 11:56 AM
  2. Minimum and Maximum points
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 17th 2011, 06:53 AM
  3. Replies: 8
    Last Post: November 8th 2010, 06:25 PM
  4. How to find Maximum and Minimum Points?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 26th 2009, 02:49 AM
  5. Replies: 0
    Last Post: November 19th 2007, 12:51 AM

Search Tags


/mathhelpforum @mathhelpforum