1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Differential calculus problem

  1. Aug 28, 2009 #1
    1. The problem statement, all variables and given/known data

    the height of a certain hill is given by

    h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12)

    wher y is the distance north and x is the distance east of south hadley

    a)Where is the top of the hill

    b) how high is the hill

    c) how steep is the hill at a point 1 mile north

    2. Relevant equations



    3. The attempt at a solution

    dh/dx=y-3x-9=0

    dh/dy=x-4y+14=0

    using linear system of algebra I find that my coordinates on top of the hill are

    (x=-26,y=-3)

    b) just plug in the coordinates you got in part a, into the h function; answer: h(x=-26,y=-3)

    c) the slope would just be the gradient of h , which is: [tex]\nabla[/tex]h=(dh/dx)x-hat+(dh/dy)y-hat=-7x-hat+11y-hat

    |[tex]\nabla[/tex]h|=sqrt(49+196)

    direction is just: cos(theta)=[tex]\nabla[/tex]h dot dl/(
    |[tex]\nabla[/tex]h||dl|), you take the inverse of cos(theta)
     
  2. jcsd
  3. Aug 28, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    In the problem it is given that the x is the distance east of south.
    Will it make any difference on the co-ordinates of the tip of the hill?
     
  4. Aug 28, 2009 #3

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Your equations look correct, but your result (-26,-3) is not....check your algebra.

    Right idea

    Check your math on that again....you are missing a factor of 20(!) and your x-component is incorrect.
     
  5. Aug 28, 2009 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    No, "x is the distance East of South Hadley"....South Hadley being the name of a town :wink:
     
  6. Aug 28, 2009 #5

    Nabeshin

    User Avatar
    Science Advisor

    To be fair, this isn't a very good characterization of the topography of the region. =( On what interval is this function valid? I get the feeling they're aiming for Mount Holyoke, simply because it's close to where the peak of the function is, though.
     
  7. Aug 29, 2009 #6

    I did check my math and I continue to come up with: [tex]\nabla[/tex]h=(y-3x-9)x-hat+(x-4*y+14)y-hat, with x=1,y=1
     
  8. Aug 29, 2009 #7

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Look at your original expression for 'h'...you are missing the factor of 10 in front and also another factor of 2 that you seem to have divided by....in part (a) it didn't matter, because you were setting it equal to zero, but here it does matter.

    Also, when you plug in (1,1) to your above expression you do not get (-7,11).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential calculus problem
  1. Calculus Problem (Replies: 9)

  2. Calculus Problem (Replies: 2)

  3. Calculus problem (Replies: 1)

  4. Calculus problem (Replies: 11)

  5. Calculus Problem (Replies: 2)

Loading...