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Linearization of an equation around fixed points

  1. Feb 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the linearization of the equation y' = y(-1+4y-3y^2) about each of the fixed points


    3. The attempt at a solution
    I think this is correct for finding fixed points:
    Set y' = 0 = y(-1+4y+3y^2), so the fixed points are y = 0, 1/3, 1

    What exactly does it mean by linearization of the equation around each of the fixed points?
     
  2. jcsd
  3. Feb 20, 2008 #2
    linearization

    the linearization of a function f about a, (linearization at x=a) is
    L(x)= f(a)+f'(a)(x-a) Its pretty much like a taylor series approximation.
     
  4. Feb 20, 2008 #3
    example

    find the linearization of f(x)=x^2 about x=3

    L(x)=f(3)+f'(3)(x-3)
    L(x)=9+6(x-3)=6x-9
     
  5. Feb 20, 2008 #4
    But using those fixed points, f'(a) would always be 0. Are those the correct fixed points?
     
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