Thread: The linear approximation of a function
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Old October 20th, 2007, 11:18 PM
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Originally Posted by Undefdisfigure View Post
Find the linear approximation of the function f (x, y, z) = root(x^2 + y^2 + z^2) at (3, 2, 6) and use it to approximate the number

root((3.02)^2 + (1.97)^2 + (5.99)^2)


Thanks.
use the formula, f(x,y,z) \approx f(x,y,z) + f_x (x_0,y_0,z_0)(x - x_0) + f_y (x_0,y_0,z_0)(y - y_0) + f_z(x_0,y_0,z_0)(z - z_0)

for (x,y,z) close to (x_0,y_0,z_0)

here, use (x,y,z) = (3.02,1.97,5.99) and (x_0,y_0,z_0) = (3,2,6)


note, f_x (x_0,y_0,z_0), f_y (x_0,y_0,z_0), \mbox{ and } f_z (x_0,y_0,z_0) are the derivative with respect to x,y,and z respectively, evaluated at (x_0,y_0,z_0)

can you take it from here?
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