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!

Find direction of tangent line to equation

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the direction of the line tangent to the curve [itex] x^4+y^4=32 [/itex] at the point [itex] (2, -2) [/itex]

    2. Relevant equations

    Anything goes, we're in vector calculus now.

    3. The attempt at a solution

    So, to find the tangent line, I was thinking of taking the gradient, but I'm not sure how to do that since the curve is in a squirrely format. I think they call that "implicit".

    Perhaps the gradient is [itex] 4x^3i+4y^3j [/itex]?

    and then at the given point we would have [itex] 32i-32j [/itex]

    Is this actually the direction of the line tangent to the curve at the given point? Is this actually the answer? I don't really know.
     
  2. jcsd
  3. Jan 29, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    No. [itex] 32\hat{i}-32\hat{j},, [/itex] is the direction of greatest slope. The tangent line is perpendicular to this.
     
  4. Jan 29, 2012 #3
    darn. so how do I find the perpendicular to that?
     
  5. Jan 29, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Rotate the vector 90°.
     
  6. Jan 29, 2012 #5

    jedishrfu

    Staff: Mentor

    Remember doing lines perpendicular to a line how did you figure out the slope?

    Negative inverse right?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find direction of tangent line to equation
Loading...