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!

Homework Help: Find Steepest Climb of this Hyperbolic Paraboloid

  1. Oct 11, 2009 #1
    Delete please.
    Last edited: Oct 12, 2009
  2. jcsd
  3. Oct 11, 2009 #2


    User Avatar
    Homework Helper

    if you define F(x,y,z) = x^2-y^2+z

    then the paraboloid is defined by the level surface
    F(x,y,z) = 0

    the gradient direction represents the direction of maximum change, and will by defintion be perpindicular to any level surface.

    how about this.... consider the function
    f(x,y) = z = y^2-x^2

    the calculate the 2D gradient
    [tex]\nabla f = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial x})[/tex]

    this will represenet the direction of greatest change of z = f(x,y), with x & y and i think it should be easy to relate the slope to the magintude of the gradient
  4. Oct 11, 2009 #3
    Thank you for the help, but one more question...
    Do I need to multiply the gradient of F(x,y) by the unit vector to find the direction of greatest ascent?
  5. Oct 11, 2009 #4


    User Avatar
    Homework Helper

    no worries, but the question you asked doesn't really make sense, as the gradient is a vector, so what do you mean multiplying a vector by a vector?

    the steps i outlined, you will give you the x,y direction, which direction of greatest ascent & the value of that slope in that direction

    if you want to find the unit vector representing the direction on surface, use the x,y direction with the slope to find a vector in that direction (in 3D), then normalise by divding by the vector magnitude

    note as a check, the vector you find will be perpindicular to the gradient you gave in you first post
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook