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">

Hey I heard you were stuck on a math problem in class today, which one was it?

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

It was $f'\left(x\right)=5x-x^{2}$

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

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

I see.

</div></div>

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

What part are you stuck on? the whole thing or completely lost?

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

I'm pretty much entirely lost...

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

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

It's ok. I'll explain it to you.

</div></div>

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

Thank you!

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

<div><img class="left"/><div class="alert gray">
First you take whats given,

$f'\left(x\right)=5x-x^{2}$
Then we We define the derivative of f with respect to x
$\lim _{h\to 0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$
produces a value for each x
at which the derivative is defined, and this leads to a new function $y=f'(x)$
then plug in your given info
$\lim _{h\to 0}\left(\frac{\left[5\left(x+h\right)-\left(x+h\right)^2\right]-\left[5x-x^2\right]}{h}\right)$ this simplifies to
$\lim _{h\to 0}\left(\frac{\left[5x+5h-x^2-h^2-2xh-5x+x^2\right]}{h}\right)$
this gets worked out to $\lim _{h\to 0}\left(\frac{5h-h^2-2xh}{h}\right)=\lim _{h\to 0}\left(\frac{h\left(5-h-2x\right)}{h}\right)$
and finally gives you $\lim _{h\to 0}\left(5-h-2x\right)=5-0-2x$

</div></div>

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

Thank you! I understand now! :)

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

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