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;
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.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;
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.right{
content:url("https://i.imgur.com/5ALcyl3.png"); width:50px;
border-radius: 50%;
display: inline-block;
vertical-align:top;
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</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>
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<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>
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<i class="fa fa-user-plus fa-2x" aria-hidden="true"></i>
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<div><img class="left"/><div class="alert gray">

Hey Gabby ! Can you explain how to do problem number 5 for section 1.8?

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Of course ! You need to remember that for 1.8 you need to understand the formula L(x)=f(a)=f'(a)(x-a).This formula is used to find the local linerization. When looking at the formula it's easier if you break the pieces apart to see what exactly you're looking for. For example you know you need to have f(x), which should be given to you. Then you know you have to find the derivative of f(x) and multiply it to (x-a).
Now problem number 5 is Find the local linerization of f(x)=x^4. Using the derivative f'(x)=4x^3 at x=2. Then use this to estimate 2.01^4.

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

I see. So the formula for L(x) would be L(x)=F(2)+f'(2)(x-2). Which should then transfer to L(x)=2^4 +4 2^3) (x-2).

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<div><img class="left"/><div class="alert gray">
After simplifying the formula would be L(x)=16+32(x-2). How do i use this to estimate 2.01^4 ?

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Perfect you're understanding it !Now to do that you would need to just plug in 2.01 for x. Your new equation will look like L(2.01)=16+32(2.01-2).Do you know how to solve this from here?

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

I think so? First I'll subtract 2.02 from 2 which would give me 0.01. Now my equation looks like L(2.01)=16+32(.01). After multiplying 32 by 0.01, I get .32. Which then leads L(2.01)=16+.32, now the solution of L(2.01)=16.32.

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<div><div class="alert blue">
Great job Trish! Exactly, the key concept to take away is to memorize the equation of L(x)=f(x)=f'(x)(x-a) in order to find your local linerization. After you have that down the rest is easy. I would say the only tricky part would be finding the derivative but you got that part right. If you need any more help let me know!

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

Thank you again Gabby, I'm going to pass that quiz now !

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