# Find the linearization L(x, y, z) of the f(x, y, z) = 8*sqrt(x^3 + y^3 + z^3) at the point (1, 2,...

## Question:

Find the linearization {eq}L(x, y, z) {/eq} of the {eq}f(x, y, z) = 8 \sqrt{x^3 + y^3 + z^3} {/eq} at the point {eq}(1, \; 2, \; 3) {/eq}.

## Linearization:

Given a function of three variables {eq}f(x,y,z) {/eq} its linearization around the point {eq}(x_0,y_0,z_0) {/eq} is given by

{eq}L(x,y,z) = f(x_0,y_0,z_0) + (\frac{\partial f}{\partial x})_{(x_0,y_0,z_0)}(x-x_0) + (\frac{\partial f}{\partial y})_{(x_0,y_0,z_0)}(y-y_0) + (\frac{\partial f}{\partial z})_{(x_0,y_0,z_0)}(z-z_0) {/eq}

## Answer and Explanation:

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View this answerFor the problem at hand, we have {eq}x_0 = 1 \\ y_0 = 2 \\ z_0 = 3 \\ f(x, y, z) = 8 \sqrt(x^3 + y^3 + z^3) \\ \frac{\partial f}{\partial x} =...

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Chapter 10 / Lesson 1Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!