Math 181 Miniproject 3: Texting Lesson.md
---
My lesson Topic
===

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

h1 {
color: green;
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://statici.behindthevoiceactors.com/behindthevoiceactors/_img/chars/michelangelo-rise-of-the-teenage-mutant-ninja-turtles-5.89.jpg);
width:50px;
border-radius: 50%;
float:left;
}
.right{
content:url(https://statici.behindthevoiceactors.com/behindthevoiceactors/_img/chars/donatello-rise-of-the-teenage-mutant-ninja-turtles-2.89.jpg); 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 bro! Mind helping me out with this math stuff (assignment)? it looks tricky

</div></div>

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

If you want I can help explain it to you. Which problem are you stuck on?

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

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

It's problem #2.
Part a) write out the limit definition of the derivative f'(x) of a function f(x)
Part b) for the function f(x)=2x^2+1, find the exact formula for f'(x). Use only the definition for the derivative.

</div></div>

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

How do I do this problem???

</div></div>

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

So what this question is asking you to do is to compute the derivative using a single point to find the formula of f'(a). Like this you can find f'(a) at any point of 'a'

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

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

Could you show me the steps pls?

</div></div>

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

K. The first thing we have to do is take the derivative of f(x) in order to get the formula of f'(x).Do you know how that formula looks?

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

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

Is it this one?$$lim(h->0)f'(x)={\frac{f(x+h)-f(x)}{h}}.$$

</div></div>

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

Exactly! That's part a) right there.Now for part b) we are trying to find the derivative of f'(x) and we are already given 'X' which we just plug into the derivative formula.

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

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

Ok I think I'm starting to get it but how do we find f'(x)
</div></div>

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

Mikey, you just plug in your f(x) equation into every x in the derivative formula to get f'(x)

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

<div><img class="left"/><div class="alert gray">
So like dis??

$$f'(x)={\frac{(2(x+h)^2+1)-(2x^2+1)}{h}}.$$
</div></div>

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

Great, now foil the 2(x+h)^2 by mutipling 2(x+h)(x+h) and the rest is simple.

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

<div><img class="left"/><div class="alert gray">
So like dis??

$$f'(x)={\frac{(2(x+h)(x+h)+1)-(2x^2+1)}{h}}$$
$$={\frac{(2(x^2+2xh+h^2)+1)-(2x^2+1)}{h}}$$
$$={\frac{(2x^2+4xh+2h^2+1)-(2x^2+1)}{h}}$$
$$={\frac{(2x^2+4xh+2h^2+1-2x^2-1)}{h}}$$
then i cancel any opposites to get:
$$={\frac{4xh+2h^2}{h}}$$
lastly I divid it all by h to get:
$$={4x+2h}$$
What do I do after that?? :confused:

</div></div>

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

Now you just find the lim from h->0 by pluggin' in zero to the h

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

<div><img class="left"/><div class="alert gray">
Is this right bro?

$$im (h->0)f'(x)= 4x+2(0)$$
$$=4x???$$
</div></div>

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

Yup! And that's all you gotta do to solve for problem 2 :thumbsup:

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

<div><img class="left"/><div class="alert gray">
Thanks Donnie! You know you're my favorite brother right?! I luv u

:kissing_closed_eyes: :rolling_on_the_floor_laughing:
</div></div>

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

Yeah yeah. Love you too bro :)

</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.