Math 181 Miniproject 3: Texting Lesson.md
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My lesson Topic
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<style>
body {
background-color: #eeeeee;
}

h1 {
color: maroon;
margin-left: 40px;
}

.gray {
margin-left: 50px ;
margin-right: 29%;
font-weight: 500;
color: #000000;
background-color: #cccccc;
border-color: #aaaaaa;
}

.blue {
display: inline-block;
margin-left: 29% ;
margin-right: 0%;
width: -webkit-calc(70% - 50px);
width: -moz-calc(70% - 50px);
width: calc(70% - 50px);
font-weight: 500;
color: #fff;
border-color: #336699;
background-color: #337799;
}

.left {
content:url("https://i.imgur.com/rUsxo7j.png");
width:50px;
border-radius: 50%;
float:left;
}
.right{
content:url("https://i.imgur.com/5ALcyl3.png"); width:50px;
border-radius: 50%;
display: inline-block;
vertical-align:top;
}
</style>

<div id="container" style=" padding: 6px;
color: #fff;
border-color: #336699;
background-color: #337799;
display: flex;
justify-content: space-between;
margin-bottom:3px;">
<div>
<i class="fa fa-envelope fa-2x"></i>
</div>
<div>
<i class="fa fa-camera fa-2x"></i>
</div>

<div>
<i class="fa fa-comments fa-2x"></i>
</div>
<div>
<i class="fa fa-address-card fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-phone fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-list-ul fa-2x" aria-hidden="true"></i>
</div>
<div>
<i class="fa fa-user-plus fa-2x" aria-hidden="true"></i>
</div>
</div>

<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"

</div></div>

<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.

</div><img class="right"/></div>

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

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

<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

</div><img class="right"/></div>

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

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

</div></div>

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

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

</div><img class="right"/></div>

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

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

</div></div>

<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?

</div><img class="right"/></div>

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

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

</div></div>

<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?

</div><img class="right"/></div>

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

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

</div></div>

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

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

To submit this assignment click on the Publish button . Then copy the url of the final document and submit it in Canvas.