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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For 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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Linearization of Functions

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Chapter 10 / Lesson 1
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Over 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!


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