Results 1 to 3 of 3

Math Help - find max slope multivariable

  1. #1
    Senior Member
    Joined
    Jun 2009
    Posts
    251

    Angry find max slope multivariable

    z=e^{-(x^2+y^2)}
    find the maximum slope and give answer in degrees

    I believe that since this is a paraboloid and is symmetrical that I can treat it with only the z and x axis. So I take the second order partial derivative with respect to x and get
    4xe^{-(x^2+y^2)}-2e^{-(x^2+y^2)} and equate it with 0. After that I have no clue how to proceed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    The function f(x,y)=e^{-(x^2+y^2)} is radially symmetric right? We can write it in polar coordinates as f(r,\theta)=e^{-r^2}
    So first find f_r, then find where it has a maximum value. That gives you the r value. But the function is independent of \theta so any \theta with that r will also have a maximum value. So the function will have a maximum slope over a circular region with radius r.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jun 2009
    Posts
    251
    I'm sorry but I haven't learned about polar coordinates. I haven't learned about vectors yet either.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 13th 2010, 04:17 AM
  2. Replies: 1
    Last Post: September 28th 2009, 10:24 AM
  3. Find Slope
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 4th 2008, 04:40 PM
  4. find the slope
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 14th 2007, 04:01 PM
  5. find slope
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 13th 2007, 04:51 AM

Search Tags


/mathhelpforum @mathhelpforum