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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">

Hi! I have a couple of questions on a problem for my calculus practice exam, I am hoping you could help. Here is the problem. "Find the local linearization of f(x)=x^(2) using the derivatice f'(x)=2(x)at x=8 then, use it to estimate 10^2"

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

Okay great! I am able to help you with this, first can you state the formula you believe we have to use in this problem.

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The formula we use in this case is y=f(a)+f'(a)(x-a)
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<div><div class="alert blue">

Great, we will solve this problem in no time. First we need to substitiue the given values into the formula. Start off with f(x) then f'(x) and lastly x=8 

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

Does that end up giving us y=(8^2)+2(8)(x-8)?

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

Yes! great job, now continue to simplify the expression. 

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

my final version of the overall expression is y=64+16(x-8)

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

Good job! That is the correct answer for the first part of the problem. Now we take into consideration finding 10^2. Do you know what we have to do next?


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

I believe we can just substitute the 10 into our expression?

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

Yes. We need to use L(10). 10^2= 64+16(10-8) and our final value for 10^2= 96. Now is our approximation too big or too small to the actual value?

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

Our approximation was too small since the actual value of 10^2=100.

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

Good! That completes this problem.
</div><img class="right"/></div>

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.



