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: Curve of intersection of sufaces, find f'(1), g'(1), x, and y. (Answers included).

  1. Mar 21, 2012 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Given that near (1,1,1) the curve of intersection of the surfaces

    x^4 + y^2 + z^6 - 3xyz = 0 and xy + yz + zx - 3z^8 = 0

    has the parametric equations x = f(t), y = g(t), z = t with f, g differentiable.

    (a) What are the values of the derivatives f'(1), g'(1)?
    (b) What is the tangent line to the curve of intersection at (1,1,1) given that z = 1 + s? (Find what x and y are equal to.)

    f'(1) = 4
    g'(1) = 7
    x = 1 + 4s
    y = 1 + 7s

    2. Relevant equations
    At least gradients, and partial derivative taking.

    3. The attempt at a solution
    I took the gradients of each surface (the first one being f(x,y,z) and the second one being g(x,y,z) respectively). I tried to set the respective components equal to each other in an attempt to solve for something but I ended nowhere useful. I also tried to think of z = t = 1 and in order to try and find x and y. Then, I was like "Oh, wait, I have a point (1,1,1), let me just shove it into the gradients." all in order to get the correct answers and then to try and make sense of what I did but I didn't succeed :(.

    Any help in solving this problem would be greatly appreciated!
    Thanks in advance!
  2. jcsd
  3. Mar 27, 2012 #2


    User Avatar

    Re: Curve of intersection of sufaces, find f'(1), g'(1), x, and y. (Answers included)

    Is what I wrote confusing or something? If it is, please tell me what to change that way I could get an answer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook