# Given f(x)=(8+x)^\frac{1}{3}, a=0; f(-0.1) i. Write the equation of the line that represents the...

## Question:

Given {eq}f(x)=(8+x)^\frac{1}{3}, a=0; f(-0.1) {/eq}

i. Write the equation of the line that represents the linear approximation of the function at the given a.

ii. Use the linear approximation to estimate the given function value.

## Estimating Function Values Using Linearization:

The equation of the line tangent to a function {eq}f(x) {/eq} at {eq}x=a {/eq} is:

{eq}L(x)=f\left ( a \right )+{f}'\left ( a \right )\left ( x-a \right ) {/eq}.

The equation of the tangent line can be used to approximate the value of the function at an {eq}x {/eq}-value that is close to {eq}a {/eq}.

## Answer and Explanation:

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View this answerGiven {eq}f(x)=(8+x)^\frac{1}{3}, a=0 {/eq}:

i. To find the equation of the tangent line to {eq}f(x) {/eq} at {eq}x=a=0 {/eq}, we need to...

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