Find the linearization of the function y = 6 sqrt{2x - 1} at x = 5.

Question:

Find the linearization of the function {eq}y = 6 \sqrt{2x - 1} {/eq} at {eq}x = 5. {/eq}

Linearization of a Function:

Linearization of a function is a way to replace the complicated function into a simpler linear function. Linearization of a function {eq}\ f(x) \ {/eq} at {eq}\ x=a \ {/eq} is a linear function given by:

{eq}L(x) = f(a) + f'(a) (x-a) {/eq}

The graph of this function is a tangent line to the graph of {eq}\ f(x). {/eq}

Answer and Explanation:

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Given:

{eq}y = f(x) = 6 \sqrt{2x - 1} {/eq}

The linearization of {eq}\ f(x) \ {/eq} at {eq}\ x=5 \ {/eq} is given by:

{eq}L(x) = f(5) + f'(5)...

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Linearization of Functions

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Chapter 10 / Lesson 1
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