Linearization homework problem

  • Thread starter DeadxBunny
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  • #1
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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?
 

Answers and Replies

  • #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]
 
  • #3
HallsofIvy
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fz(1, 1, pi/2)= -pi/2, not pi/2.
 

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