# 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}.

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Given {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...

How to Estimate Function Values Using Linearization

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Chapter 10 / Lesson 2
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Sometimes landing on Mars isn't that easy. You might need to use linearization to estimate if you will crash into the planet, or miss it entirely. Learn how to do just that in this lesson.