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: Linear approximation

  1. Feb 1, 2012 #1
    Find the linear approximation to the equation f(x,y) = 3 sqrt((x y)/4) at the point (2,8,6), and use it to approximate f(2.28,8.22). I know you take the derivative of fx(x,y) and fy(x,y), I think I'm taking the derivative wrong. Then after that you put x and y in the equation and solve for fx(2,8) and fy(2,8). Then take f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b). For fx(x,y) I'm coming up with .75(y/4) and for fy(x,y) I'm getting .75(x/4)
  2. jcsd
  3. Feb 1, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your derivatives are indeed wrong. Let's start with a simpler function of just one variable.

    [tex]g(x) = 3 \sqrt{x / 4}[/tex]

    What is [itex]g'(x)[/itex]?
  4. Feb 1, 2012 #3
    g'(x)= [3(x)^-.5]/4
  5. Feb 1, 2012 #4
    Want to know an easy way to derive a linear approximation equation? Well, I'll give you some intuition: it's basically the same thing as the tangent line equation in so many words.
  6. Feb 1, 2012 #5
    L(x)= f(x) + f'(a)(x-a)

    (2.8,6) is the point...and so on
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook