Math 181 Miniproject 3: Texting Lesson.md
---
Differentiable!
You're continuously killing me!
===

<style>
body {
background-color: #eeeeee;
}

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

.gray {
margin-left: 50px ;
margin-right: 29%;
font-weight: 500;
color: #FFF;
background-color: #F08080;
border-color: #F08080;
}

.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: #000;
border-color: #48D1CC;
background-color: #48D1CC;
}

.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, you look a little confused... do you need help on a problem?

</div></div>

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

YES! Please! I can't seem to get the concepts of a function being differentiable and a function being continuous straight! The more I read, the more lost I get!
:(

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

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

No worries. Let me first explain what a differentiable function entails and what a continuous function is. A function is **DIFFERENTIABLE** so long as there is an existing derivative for each point comprised within that function's domain. In order for a function to be **CONTINUOUS**, it must adhere to the three following conditions:
*1. f is defined at a.*
*2. f has a limit as x approaches a.*
3.$\lim\limits_{x\to a}$ f(x) = f(a)

This ultimately results in a function that, within its domain, when sketched, it is done in one continuous motion. The correlation between these two concepts is when a function is continuously differentiable, occurring when f is differentiable and its derivative is continuous.
</div></div>

</div></div>

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

Can you give me an example of each one on a graph?

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

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

Sure!
So here we have an example of a graph of a function that is continuous:

And here is a graph of a function that is differentiable:

</div></div>

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

What would be an example of a continuously differentiable function when graphed?

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

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

A continuously differentiable function would look like this:

</div></div>

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

Oh I see! Thanks for for the help!

</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.