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Linearization homework problem

  1. Nov 16, 2004 #1
    Original question: Let f(x,y) = ln(xy) + yzcos(xz). Find the linearization of f at the point (1,1,pi/2). Use this linearization to estimate the change in the value of the function resulting from moving from (1, 1, pi/2) to (1.1, 1.2, pi/2 + 0.2).

    I believe the first steps to completing this problem are finding the partial derivatives of x, y and z at the point (1, 1, pi/2) which I have done:
    fx = 1 – (pi/2)^2
    fy = 1
    fz = pi/2
    Are these correct?

    If so, what do I do next?
     
  2. jcsd
  3. Nov 17, 2004 #2

    Tide

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    You just need to use this:

    [tex]f(x, y, z) = f(x_0, y_0, z_0) + f_x (x-x_0) + f_y (y-y_0) + f_z (z-z_0) +O(\Delta^2)[/tex]
     
  4. Nov 17, 2004 #3

    HallsofIvy

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    fz(1, 1, pi/2)= -pi/2, not pi/2.
     
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