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Math 181 Miniproject 3: Texting Lesson.md
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My lesson Topic
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<div><img class="left"/><div class="alert gray">

So... what exactly is this assignment? it looks tricky.
$a)$ Use the derivative formula $f'(x)=4x^3$ to find the linear approximation of $f(x)=x^4$ at $x=2$. $b)$ Use the linear approximation to estimate the value of $3.06^4$

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Oh! Do you remember the lecture for 1.8 that we did in class friday?   

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I kind of remember... but can you refresh my memory? 

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What is $L(x)$?

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So, in class for section 1.8 we talked about using the derivative of an equation to find the linear approximation which is $f(x)=L(x)=f(a)+f'(a)(x-a)$

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Oh right! Do we just plug in our values from the question since they give us the values in the question?

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Yes! you got it. :smile: For part $b)$ of the problem you would just plug in the given value for x into the linear approximation you just did. 


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Alright so the equation would look like this?
$L(x)=f(2)-f'(2)(x-2)$
So..
$L(x)=16+32(x-2)$

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Yes! 
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Also, don't forget to plug in your value into your linear approximation to estimate the value of $3.06^4$

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<div><img class="left"/><div class="alert gray">

Like this? $L(x)=16+32(3.06-2)$
Which is $49.92$. 

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<div><div class="alert blue">

Awesome! you totally got this :100: 

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To submit this assignment click on the Publish button ![Publish button icon](https://i.imgur.com/Qk7vi9V.png). Then copy the url of the final document and submit it in Canvas.



