my portfolio

this has been quite an adventure, there has been laughter, and sadness, and beauty and ugliness, and we all learned something in the end. like a 90’s after school special. at the beginning of this hot mess of an assignment we set out with 7 goals. and now that the semester is coming to a close i’m wrapping up my adventure with the math blogs as best i can.

goal 1.

critical thinking skills

defined as such…

“Ability to use and manage intelligence and skills appropriately for tasks or goals across all four domains of knowledge” (google dictionary)

im not sure what the four domains of knowledge are, i suppose writing, math, science, and history but i could be way off. i kinda feel like this is one of those things that no one person can really pin down, everyone will have a different opinion about what qualifies as critical thinking and what doesnt. in my own opinion i think that in almost every post, with my examples and how i showed step by step how to do the problems is critical thinking. even though i feel like i did this in all of my tutorials i dont think i really improved it much. see for yourselves this is my first post…

https://vannasblog.wordpress.com/wp-admin/post.php?post=5&action=edit

and here is my most resent…well after this one your reading of course.

https://vannasblog.wordpress.com/wp-admin/post.php?post=267&action=edit

 

goal 2.

metacognitive skills

defined as…

“Allow the individual to evaluate and think about their own as well as others’ knowledge and understanding^15” (google dictionary)

okay with this one i just really tried to make my tutorials slow and simple and easy to read. i used lots of pictures and jokes to help my reader remember the examples and did my best to mix easier problems with progressively harder ones as the tutorial continued.

such as with my optimization problems i dedicated 3 posts to each different type of problem given.

(1) https://vannasblog.wordpress.com/wp-admin/post.php?post=254&action=edit

(2) https://vannasblog.wordpress.com/wp-admin/post.php?post=262&action=edit

(3) https://vannasblog.wordpress.com/wp-admin/post.php?post=267&action=edit

 

goal 3.

communication skills

okay well ive always been a good communicator. ive taken years of speaking and writing classes and had a really great head start in this project because of it. this post below was just me trying to engage my readers and make them see how much fun this blog project could really be. its a story called the math quest and its about a math teacher who’s out there looking for another nerd like her to talk about math and whatnot together. but she makes it increasingly difficult to do so by giving her phone number in a math equation and her address in a function.

https://vannasblog.wordpress.com/wp-admin/post.php?post=90&action=edit

 

goal 4.

technology skills.

i was really scared about this one because im sooo bad with technology. but im really proud of myself, my boyfriend (well fiance as of about a week ago) really helped me get creative with this. he showed me how to use paint and who to pictures from google on my blogs and how to do links and all sorts of crazy stuff. but as far he taught me something i learned that much more about it by myself.

such as with paint. he just showed me the program. but all the stars and faces and the cropped pictures in them were all me.

https://vannasblog.wordpress.com/wp-admin/post.php?post=225&action=edit <– this is one of my favorite posts with paint.

https://vannasblog.wordpress.com/wp-admin/post.php?post=191&action=edit <– this was my first post with paint.

 

goal 5.

creative engagement with the material (having fun with it)

dont make me laugh mrs. macinnis. this project was always a bit of a laugh for me. starting from day one when mrs. macinnis said use you best judgement in what pictures or with the things you write about. and she gave the example of posting cat pictures as not being about math unless maybe one is cutely sleeping on your math book. so i posted a picture of one sleeping on the computer because that’s where all of our homework is done. i think i really showed my silly side with the last few posts of mine. the optimization problems. because mrs. macinnis kept over hearing me and friends talking about how the cows in her problem could easily escape. so i was like well vampires can’t cross running water and what about if theres a piranha in the water?

https://vannasblog.wordpress.com/wp-admin/post.php?post=254&action=edit

https://vannasblog.wordpress.com/wp-admin/post.php?post=262&action=edit

https://vannasblog.wordpress.com/wp-admin/post.php?post=267&action=edit

 

goal 6.

tinkering

hmm. well im not sure i really did this one. tinkering might just be something  was avoiding in this project because i wanted my readers to understand the material not to be so much impressed by my great and powerful adventuring skills. in this post (below) i introduced a website that will check your algebra for you and told everyone that i use it in just about all my blogs because i want to be reliable. not to say that a little exploring is bad, im not, i mean i learned a whole new program that i had no idea my computer even came with (paint) and i did learn how to speak latex. i guess that counts kinda.

https://vannasblog.wordpress.com/wp-admin/post.php?post=71&action=edit

 

goal 7.

a sense of contributing. i have read through every blog since the project started. i even commented on the ones that really blew me away. i have 6 posts on my blog and every time i got a new one it just made me feel like i was doing something useful just by doing my homework. i even had one girl say she has my blog on her rs reader (whatever that is). me and my friends even bonded by laughing about the blogs and telling each other “hey get off your lazy butt and do them so you can make a good grade” 3 out of the 4 of us followed through on the blogs so i guess laughing and yelling at each other kinda contributed to us following through on the project.

 

all in all, im glad that i did this project. it was a lot of work and made me want to pull my hair out sure, but im better because of it. it forced me to study because not doing this blog is like missing an exam because of how many points its worth. i wish more people had followed through with it because all it did was help in the end. i really hope that when i take calc 2 that ill have a teacher who cares enough about her students wellbeing to some creative assignments like this one. its been great and terrible mrs. macinnis. 🙂

last type of optimization problem

okay so you are a spanish cartel member and you need to transport…um some questionable materials, you fancy yourself a business man and don’t want to pay a lot on shipping it, so you get some boxes together, you take a square of cardboard that is 16 inches by 16 inches. how big of a square should you cut to maximize your volume?

you should really get out of the cartel man. its bad news. go find a nice job in the city. mexico is beautiful and you could be make in twice what your making now.

anyways…

this is your box. shut up rainbows are pretty! 😡

you need the volume equation wich is L*W*H

so

now take the derivative…

next plug in to the quadratic equation

   or 

x=2.666   or   x=8

disregard 8 because if you cut 8 inches from both sides you end up with negative box. and that’s not useful at all.

so by cutting 2.666X2.666 squares from each side will give you the maximum volume you need to transport those questionable materials. now hurry up and send them out before the boss gets impatient.

optimization

so im back from a lovely weekend of birthday festivities. 🙂 got myself some chill pills at the paper bear special for the final lol… there ice cubes. 🙂 very cute right?

so anyways another optimization problem!!! now with unicorns!

you are a unicorn breeder. three lady unicorns just had 4 little baby unicorns, ALL ON THE SAME DAY!! so needless to say you need to prepare 4 new pins for them.

you have 3000 square yards of space for the 4 pins how much cloud fence will it take to create the new pins?

first things first.

how on earth did you get your unicorn? because i have been looking for years you jerk and now i find out you have an overige of unicorns! share!!! >:C

secondly, we need to make some equtions to help us find y.

<—area formula

beautiful, now lets do some quick counting to know how many x’s and y’s we have.

we have 5 x’s and 2 y’s

so our equation looks like so…

so now we replace or eqation thats equal to y…

next take the prime and set it equal to zero.

now to find y all we have to do is plug in x and solve in the original equation.

x=34.6 and y=86.7

optimization

so i had a few issues with mrs. macinnis’s word problems she gave us for optimization. one being that cows can swim!

so i wrote my own awesome problems 🙂 lol

you are a fearless vampire hunter (especially of sparkly vampries) and you just cough one terrible scurge of socity. you need to get him into a cell to keep him until the sun can do its trick. you have 12,000 square meters of land dedicated to your craft that you want surrounded by reniforced steel. you decide to taunt him by putting the cell next to a river (everyone know vampires cant cross flowing water) what dimension will minimize the fenceing needed(cus that reniforced steel is expensive).

first things first we need to make our equations.

we want to minimize fenceing it takes to get arounf the 12,000 square meters of land so in order to do that we need the area formula. which is just length times width.

now to slove for something when there are 2 variables we need to substitute in something thats equal to the variable were substituiting.

now that we have our y, we are going to put it into the parimiter formula P=2x+y

now to get your y value you need to put the x value in to the original function

y=154.93

 

and there you go, its only 30 minutes until the sunrise so you sit down on your poarch to enjoy he show. all in a good nights work 🙂

have a good weekend everyone! 🙂 starting tomorow my mom is comeing to visit me cus my birthday so its going to be an extra fun weekend 🙂

 

absolute extrema contiued!!

here’s just some more practice for finding absolute extreama.

also if you were wondering these examples are from the notes from class. not because im lazy but i tried to make them twice and i messed them up so i gave up and just decided to go over the ones in the notes.

but im going to make them more colorful cus i love paint 🙂

isn’t it soooooo pretty? 🙂

kay so i need to defiantly tell you guys some rules to remember.

1. if the end point is with in ( ) or ( ] then that means that point can’t be included. so lets say the highest point is 10 and the end points are [10,-10) that means that the there just isn’t an absolute max because Mrs macinnis said that .999 repeating is equal to 1. (heresy but who am i to argue with college calculus professer.)

2. for the love of god dont make the stupid mistake of plugging in to derivative, plug the x-values into the original function.

3. just calm down and focus its the easy half of the exam 🙂

 XD LOL this little baby is sooooo cute.

absolute extrema!!!

okay so first off lemme just lay down the law here, a local max/min is different from the absolute extreme. where a local max/min is just every crest and trough of the functions graph a absolute extreme is the highest or lowest point in the funtction within the domain.

EX:

easy to find when its a graph but most likely were going to end up haveing just the function. dont worry ill show you guys how to solve one like that. 🙂

EX:

           [-3, 6]

there are two possible points that could be the absolute extrema, end points and critical points. you will probably be given the end points so i’ll show you how to find critical values…

first find the derivative.

then set it equal to zero and solve

 

now that you have the 2 types of points, set each for x in the original function!

after you set them all into the original function, you have the f(x) values of…

x |  -3   -2    4    6

f(x)| 23  33  -7  -31

the absolute max is 33 at x=-2

and the absolute min is -75 at x=4

🙂 easy peasy, and the best part about these is that they dont get too much harder. as long as you can find the derivative your good. like i said brush up of the rules and dont forget plug in the x values into the original function! good luck tomorow guys 🙂

lucky cat 🙂

 

curve sketching contiuned!!!

i promised in my last post that i was going to show you guys a function that has all the things in it! so let give this a whirl…

took me a while but here is the biggest pain in the butt problem ever.

 

the domain is all real numbers except for x=3 and x=-3

okay so we have 2 vertical asymptotes at -3 and 3. but we also have a horizontal asymptotes at 0. and the ND above the 0 in the sign chart can only be a sharp point because its still continuous there. 🙂 so lets plot our points and make dotted lines to remember where the asympotoes are.

okay lets go ahead and note that the second derivative is positive everywhere, this means all the lines are going to be a smily face concavity (concave up).

lets plot out our lines now 🙂

and there you go 🙂 a hot mess of a problem but definitely good to look over.

 

 NOW GO MY FRIENDS! go out and study! 🙂 lol

curve sketching!!

in wake of empeding doom i look out upon my brothers and i fear we are not ready. lol enough messing around! 🙂 so our exam is monday! i for one am looking forward to it, lookng forward to enighlateing it!!! i have been hard at work studing for it!

and im just nice enough to share with all of you, my friends, the answers to the exam!!!!!! hehe just kidding, 🙂 but i am going to throw down some cold hard facts about curve sketching and then later tonight some even colder even harder facts about absolute extrema. lol okay before the nyquil makes me too silly. (yeah im sick again)

 

curve sketching is exactly what the name emplys, its the sketching of curves. 🙂

you should concider the following.

1. IS THE FUNCTION CONTINOUS?

2. is the domain(-∞,∞) if not then ajust acordingly.

3. asymptotes?

4. plot any given points. (ms. macinnis is cool, shes probably going to give us some)

5. first derivative (brush up on the chain, quotient, and product rules, youll need the derivative to know where the graph is increasing or decreasing)

6. second derivative. (dont skip this one!!!! you need t to dicover concavity)

7. discontinuities (jump point and vertical tangent lines (remeber you can cross horizontal tangent lines))

8. sharp bends, or curvy

it looks like alot of work, but it isnt too bad once you actually get started. 🙂

speaking of…

lets say i gave you a problem like this 🙂  jut asume it has a domain of (-∞,∞)

first lets plot the points 🙂 ill use red cus its such a pretty color.

next lets note that the function is increasing until 0 and then is decreasing until 4 then is increasing for the rest of the function

also lets note that the function is concave down until 4 (i remember this as the frowny face concavity) and then concave up for the rest (smily face concavity)

with this information you can make the graph 🙂

congrats 🙂 you just sketched a fine curve there. in my next blog ill be posting ill talk about sharp points and ill throw in some limits. lol i know your super excited to do some like that 🙂 but dont worry their not so bad.

 

 super scary right! 🙂 zombie ate my brain is a good excuse to get out of an exam.

relative extrema!

first of all what is a relative extream?

well there can be a relative(AKA local) min and a relative max, and the easiest way i can put this is that they are the crests and troughs of the graph.

isnt my pretty drawing helpful? 🙂 again it was made in paint.

now its easy to find the mins and the maxs of a graph like this, but what if you only have a sign chart or even scarier what if you only have the function?

never fear,  🙂 i got this. lets scribble out a graph. it doesnt have to be exact just enough to see where we have mins and maxs. (oh yeah this means yet another lovely artwork be yours truly.)

can you find them? 🙂

good work! 🙂

but thats still just the easy stuff! what about if you need to find the extrema from a function alone!

first things first we need to make a sign chart! so we need to find the critical values, and to d that we need to find the derivative.

dont derivatives just always make functions look nicer 🙂

okay! next up is to set it equal to zero.

so theres your critical point. now we need to test both sides…

now we can make the sign chart.

beautiful 🙂 from this we can find the relative extrema, but wait?! theres only one critical point! does that mean theres only a local minimum at -3?

nope 🙂 the local maxs are at positive and negative infenity. 🙂

  more truths 🙂 this picture was drawn by hjstory not me 🙂

increasing and decreasing functions

 okay guys sign charts! 🙂 look at my cute ms paint skills.

today im going to teach you guys (just in case you forgot) how to draw sign charts! 😀 this is gonna be colorful…

in my little drawing here, i graphed the function…

just to make it a bit easier to follow along. 🙂

however on tests and what not you probably wont be so lucky to have the graph so ill teach you how to find where the function is increasing and decreasing without the use of the graph.

first find the derivative.

next set the derivative equal to zero. this is done so that you can find whats called a critical point. which cn also be places on the chart where the graph is undefined. that’s usually a sharp point or type of discontinuity. but were not going to worry about any of that mess because my example is just a nice easy parabola.

$latexf'(x)=2x+2=0$

so our critical point is -1 yay!

done? nope now we have test both sides, first with a number bellow -1 and then with one above -1. lets just use -10 and 10 because their easy 🙂

now we don’t really care what numbers we end up with, just whether or not there positive or negative. the -18 tell us that everything to the left of -1 is going to be decreasing and the positive 22 tells us that everything to the right of -1 is increasing.

 no cats today! just some truth.