Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number 3.022 + 5.992 + 5.972 . (Round your answer to five decimal places.)

f(3.022 , 5.992 , 5.972)=80.7

Step-by-step explanation:

Linearization of Multivariable Functions

Let f be a function that depends on the independent variables (x,y,z) and assume the following partial derivatives exist:

The function f can be linearized around a known point (xo,yo,zo) by the equation:

Given

Evaluating in (3,6,6)

The partial derivatives are

Evaluating at (3,6,6)

Evaluating at (3,6,6)

Evaluating at (3,6,6)

The linearization of f is

Operating

Using the linearization to find f(3.022 , 5.992 , 5.972)

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step-by-step explanation: