Results 1 to 3 of 3

Math Help - Cylinder rate of change problem.

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    95

    Cylinder rate of change problem.

    I'm trying to solve the following problem:

    Consider a cylinder of radius 5 whose axis is along the z axis.
    i) what is the rate of change of f(x,y,z) in the direction normal to the cylinder at the point (3,-4,4)?

    In the previous part of the question I was asked to find the grad of f = ln(x^2+y^2) + z but I cannot tie this in. I know that the equation of the cylinder is simply x^2 + y^2 = 25.

    Any help would be much appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2009
    Posts
    226
    The rate of change in a specific direction (directional derivative) is the gradient dotted with a unit vector in that specific direction. That's why the previous part of the question asked you to find the gradient. Now, find a unit vector in the direction of normal to the point (3,-4,4). Then, dot the gradient with that unit vector.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,418
    Thanks
    1854
    And, when you write a surface as f(x,y,z)= constant, \nabla f is normal to the surface at every point.

    Here, your surface is given by f(x,y,z)= x^2+ y^2= 25 so \nabla f= 2x\vec{i}+ 2y\vec{j}. Evaluate that at (3, -4, 4). Don't forget that you need a unit vector in that direction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 20th 2011, 02:47 PM
  2. Replies: 3
    Last Post: April 12th 2011, 10:51 AM
  3. Rate of Change Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 19th 2010, 09:35 AM
  4. Rate of Change - Volume and Surface Area of Cylinder
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 29th 2007, 02:49 PM
  5. Rate of change problem - please help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 25th 2007, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum