Optimization Problem #1

[jackieechu]

i have a math final tomorrow (: thank you for posting up these videos!

[ronmascara]

nice stick figures haha :P

[OoloOoly]

why we can't get dimensions of rectangular direct way ?

by

taking the area : 1000=x.

and I think the rectangular is square ,I was concluded this from the Q . so x=y

1000=x power 2

is it correct?

[janialopez4242]

thank you so much

[Nafisatzc]

omg Patrick .....if I do well in ma AP xam,,,a large part of d credit goes to U....:)

[patrickJMT]

@Nafisatzc good luck! : )

[Nafisatzc]

@patrickJMT thnx :)

[10Nasser]

thank you but i think it become as

I think it is square now but it's not a rectangular and whether the solution remains valid

[OoloOoly]

@10Nasser

the square is type of rectangular

[MadLinkzProductionz]

You are awesome!! >.<

[Loggs777]

My BC Calc teacher showed us this video in class today. You, Sir are a genius... Whole class understands it now.

[patrickJMT]

@Loggs777 wonderful : )

[duderocker1192]

lol the funny thing about my rectangle is that its a square

[o0starrynight0o]

My final is tomorrow, your videos have helped me study and clear up what my teacher made complicated. Thank you very, very much.

[Bromeu57]

Thank you so much! This is the exact problem in my book that I need help with!

[869749856]

This is how education should be. Simple, straightforward, accessible to those that really want/need it.

[brittlette14]

dont forget units!!!

[was2911]

I thought I should let u know, I LOVE YOU Thanxxxx :)

[Aiziah09]

Hmmm I'm just wondering don't you have to put +/- infront of the square root???

[Master1906]

@Aiziah09 As I just said to the other guy, there's no such thing as 'minus sqroot 1000 meters'. Unless you're living in cuckoo land, there's no need.

[OoTFanboy]

Well, everything my teacher said made no sense today. Thank you so much Patrick. All day in class I was just thinking, "ugh.. once I get home I'll just watch patrickJMT and get this instantly," and I was right!

[patrickJMT]

@OoTFanboy : )

[dotdelusion]

@OoTFanboy Me too!

[joelmartinez625]

@gogooma95 You wouldn't maximize the perimeter, think about it it doesn't make any sense to do that

[KidKlassic91]

I wish I found this in the beginning of the semester. If I pass calc one I'll never take your help or YouTube for granted.

[Cakeries]

shouldnt it be X= (+-) the square root of 1,000?

[Master1906]

@Cakeries Would a length ever be 'minus sqroot 1000'? There's knowing how to do maths, and common sense. Good to have both.

[Cakeries]

@Master1906 I know that a length can;t be negative but mathematically the square root of 1,000 is (+-). If this was an AP test and someone wrote that x=(+-)the sq.root of 1,000 they would have gotten points off, thereby i feel that he should have mentioned that answer and said that it can only be positive.

[Kalen1457]

I wish I knew of these optimization videos earlier before I completely got the question completely wrong on the test!

[110arian]

The whole day I was saying to myself that I'll fail my tomorrow's test, but now after watching all your videos I don't think I'll fail it, even if I get a low grade :)

[eyeheartthekillers]

why do you need to do the increase/decrease within the interval thing? i don't see the relation to get the dimensions

[achicklol]

@eyeheartthekillers So you know that it is a max or min (as large as possible or as small as possible)

[eyeheartthekillers]

@achicklol thank you!

[goodpinoyboy]

Thanks :)

[kenneth12345678910]

Yes hahahaha I understand it, it's like an orgy for my brain.

[violavirtuoso17]

hey, you're a lefty, right? that's why you're so smart! haha, kidding. just a joke my friends and i have... i'm not a lefty, so you know. these videos are great, you make it very simple and easy to understand. thanks so much, you saved my life!!

[bdimmortal3]

Thanks for making this video because I would not have been able to finish my homework without it

[FuntFarter]

Are you God?

[23SuS23]

i love your videos, so so so so helpful.

and your handwriting, it's awesome!

[grandmasternmk]

Thank you for explaining everything so clearly. Learning by watching your videos is much more efficient than learning by staring at my textbook! haha..Thanks again.

[6BURG9]

i was literally doing this question for an assignment last week and i was stressing because the dimensions didnt make a rectangle haha

[gogooma95]

uhh would it be different when your looking for Maxmum value?

[patrickJMT]

@gogooma95 nope

[sarahgee1300]

what if you were trying to find the MAX of this problem? you only found 1 critical point and it happened to be the minimum. There must be a maximum solution to this problem, right? Please explain. Thank you!

[patrickJMT]

@sarahgee1300 what would the max be? why must there be a solution to that?

[HBMAN1995]

@sarahgee1300 To my understanding, if you're looking for, say, the Max, but the only critical value you find yields a min, then the Max DNE. Correct?

Just a student here, could be wrong.

[patrickJMT]

@HBMAN1995 yup

[sarahgee1300]

@HBMAN1995 i think that is right - thanks!

[zarquirian1]

@sarahgee1300 hi! I'm just a student too, and i get your confusion. Some problems don't have minimums, and some don't have maximums- think a parabola. This problem is like that.-the max DNE. Because he got a negative slope on the left side, the problem is descending before the slope evens out (at the minimum) and becomes positive. Because the slope is positive and doesn't ever change back to negative, There is no maximum- it keeps curving upward towards infinity.

[sarahgee1300]

@zarquirian1 thanks! You are correct. 

[JohnnyHoot1]

I don't like how you completely change pages, would be easier to follow if you had one long piece of paper and kept going down as you worked

[patrickJMT]

@JohnnyHoot1 i don't care.

[QQLePewPew]

3:27 tea pot in the background!!! maybe?

[joejar77]

You are apparently really popular in my calculus class. I made a recommendation to another student that was having difficulty with a few issues to check out your videos. Two different other students who were nearby chimed in and they also follow you! That was a few weeks ago. Today, another completely different student told me about you (I already knew, of course). You have helped me out a ton! Thanks

[patrickJMT]

@joejar77 that is totally awesome : ) thanks for spreading the word!

[TRlPZ]

This is so weird.... the example problem you used was the exact problem I was on for my assignment... It's a sign.

[baydood510]

i don't get why you got 2x^2? i know you multiplied across...but why? could you have left it (2-2000)/x^2 and still figured it out?

[fencer5017]

@baydood510 the answer is no you could not have because you have to make it so that you are not changing the number itself you see if you have 2x^2/x^2 then it winds up equaling 2 where if you have (2-2000)/x^2 when you separate it out you get 2/x^2 which is a number that does not belong in the equation and you would get a wrong answer. Hope that helps :)

[shanniechen]

what if you use the 2nd derivative test to prove that this is a min point? P'' = 2000/x^3. and if you plug in sqrt(1000), P'' is bigger than 0 . that means it's a maximum point?? ): I'm pretty confused

[shanniechen]

opss sorry I get it already!

[TylerVallier1]

You wouldn't be as popular if you were right handed

[dapontee]

my savior!!

[bpsl888]

omg this saved and cleared the stress out of my mind. THANK GOD YOU'RE HERE!!!! :DDDD

[ian559fresno]

I got a 89 on my AP Calc BC test and I used your videos since I was absent on some lessons! Thanks SO much!

[seifdeiab]

thaaaaaaaaaaaaaaaaaaaank yooooooooooooou. but shouldn't x= + - square root of 1000?

[n3xtx]

@seifdeiab dimensions can't be a negative number

[Marcuzzorox]

@seifdeiab keep this in your mind:

sqrt (100) = |10| which is 10.

but if x² = 100

it means |x| = 10

so x = 10 or -10

which is a bit different :)

[teppeinokanojo]

lifesaver!!!

[Paputsza]

O.O I think zero was the answer for the minimum and the other number was supposed to be 500. I think you found the max.

[Wemadesomevideos]

@Paputsza A rectangle with width 0 wouldn't result in any rectangle at all, though. And at 5:10 he proves that it's a minumum. And while sqrt 1000 might feel like 500 (to me, I always think it's 100) if you square 500 it's decidedly higher than 1000. I'm pretty sure he did everything right.

[DeathRapiest]

I don't understand how you got from:

P=2x + 2000x^-1

into:

P=2 - 2000x^-2

Can you explain this to me? Thanks

[bd6m20]

@DeathRapiest @DeathRapiest

derivative of 2x = 2 derivative of 2000x^-1 = (-1) (2000) ^ (-1 - 1)

P= 2 - 2000x ^-2

[maxsmouha]

you just made my day sir

[Raymondlk]

I LOVE YOU!

[saaddaahmed]

you are like superman, doing nice things for the world simply because its in your nature. if only the world had more people like you in other fields

[troubleshooter321]

Patrick... I enjoy your vids. I saw the problem and new it was a square and thought

lxw =1000 which in square is x times x which is x squared. Take the square root of x suared and voila you have the side of the square.

[masterofdaownage]

he just proved a rectangle is a square.

[hannah1214]

you're the reason why I'm not failing in my calculus class. thank you. really :)

[GangstaShit187]

I hope you can help me with this question:

A window of perimeter L meters consists of a rectangle surmounted by an equilateral triangle. Find the width of the window that admits most sunlight.

Can you give me some hints on how to solve this?? Pretty Please.

[ooweirdoo]

ap test tomorrow LALALA

[njelyka]

You are quite helpful, sir, and are greatly appreciated.

[warmachine10461]

hey Patrick, I got a question. If u take any number greater than square root of 1000, doesn't the P' get negative, not positive?

[gouzbekistan1]

6 people dont know how to find dimensions of a rectangle with area 1000m^2, whose perimeter is as small as possible

[anguskangus]

Because of you I understand what's going on :P

[58fubu]

calculus exam today...after 16 weeks of lectures im finally understanding this stuff...thanks alot man...ur awesome...

[theunlistedmuffin123]

ap exam for calc tomorrow. good review videos, bro

[Musiclo0ovee]

PATRICK YOU ARE THE BEST

[johnnyr0cket]

dood you are my god!!!!

im not worthy.....

[retc90]

dude im not gay but i think i love u !

[libb93]

thank you so much for all your videos!!!!!!!!!

[greenee111]

I LOVE YOU

[00LhieHyunAe00]

nice one...it helps a lot!!! THANK U SO MUCH! :D

[Morgam06]

Finally somebody who explains why P'=0 is the optimum, My idiot lecturer said, when I asked, "It just is..."

[xjustxanotherxgearx]

These videos have been some serious help! Thanks!

[yur1slavio]

Thank you, was stuck on the derivative for a while but this video helped

[fitimio001]

Dude thats a square~!

[BenGonz91]

I was just doing a homework problem almost exactly like this one and this video was the only reason I figured it out

[argstupidcomputer]

If I ever become the architect I aspire to be, I'll name a bridge after you

[adamisrael86]

THANK YOU FROM ISRAEL!!!

[bmachiavelo7]

You have officially replaced my real math teacher. My scores on tests dramatically increased when I stumble on your channel! Thanks!

[zaz3r]

Thank you for these high quality videos!

[dajakesta1234]

if u sell ur vids ur gonna b rly rly rich :D

[patrickJMT]

@dajakesta1234 @dajakesta1234 ha, not quite. they are already all here for free! of course, i guess i could take all the free videos down and charge for them (had offers from education companies to do this), but i do not want to do that. my intent is to create free content to help everyone, not just those with the $ to afford it. so, that is what i am doing : )

[dajakesta1234]

@patrickJMT wow ur da best :D

[omgpwnd]

@patrickJMT exactly, and I appreciate the videos being on here, being free, and being well done. if I had the money to buy math videos I would just hire a damn tutor but, alas, I am broke.

[chbobcats20]

@patrickJMT essentially.........thank you for not selling out and offering your gifts to us students for only the price of watching an ad rather than a price that comes out of our pockets.

[johnytornado]

@patrickJMT and your videos are much appreciated!!!!

[fsuchoppa90]

@patrickJMT way to not sell out haha

[girlwiththehijab]

@patrickJMT Thank you for that-for not taking them down and having education companies sell them; It makes me hate the commercials less and I definitely understand why the apps aren't free. That's very considerate of you, especially seeing as how much they help everyone, I bet lots of people would have actually bought them (those who had the money).

[SinedReaper]

@patrickJMT and godbless you for it, its lucky and a bit ironic , that one of the best teachers iv ever seen is also free and has good intentions , once more thank you for what you do and never stop

~Also you should atleast conisder donations = )

[lenahmata]

@patrickJMT that is so nice of you patrick. godbless you :)

[vijayk925]

@patrickJMT you're a wonderful human being Mr. Patrick. God bless you and your family.

[hassananjum]

6 people need to get a life.

[Beatle214]

thanks for the upload!!

[shippo915]

dude! these are awesome!! haha

[FOULTHY]

wtf i ment to put opticnation lol

[mielo101]

thank God you also teach Operational research!!! i feel so relieve..please post more teaching on this subject. i would love to learn more about it. tq patrick.. :D

[MsMajorK]

youre a lefty, i bet you get sharpie smudgies on the side of your hand a lot. =P

[shelbieeex3]

I think your videos are the only reason why I'm going to pass my AP Calc final.

[patrickJMT]

@shelbieeex3 hope the test went well!

[qingian]

you are fucking brilliant. i'm listening to your videos as a way to study for my final tomorrow. haha

[itzzy018]

to anyone who can help:

calc problem: A 400 meter long running track is to be constructed with two parallel straightaways of length s joining two semi-circular curves of radius r. what are the dimensions of the track that will enclose the largest infield area?

i'm so confused :( if you could help me that'd be great!

[dbzhero007]

I dont really post comments on videos on youtube, but I really have to say thanks for uploading this video. It really helped me a lot! You're actually a better teacher than my calculus AB teacher haha! Thanks again =]

[yehya96]

lmfao i dont know why im watching this (:

[VantageX4]

you've got a real monopoly on the calculus videos around here. well done! i must say you have a great disposition for teaching, though you probably know that.

[patrickJMT]

@VantageX4 well, i do not know about a monopoly; there are actually a ton of others doing math videos now as well. but i would like to think mine are pretty good which is why they get the views! : )

[MrHoffmannTaiwan]

@patrickJMT What makes you so great as a teacher is that there is not a hint of sarcasm or condescending attitude or any sort of superiority attitude that so many math teachers have. You are the quintessential teacher, people love your unassuming approach and speech, I am a huge fan and recommend you every chance I get. You are a GREAT TEACHER!

[onewinged117]

@VantageX4 Sorry this was bugging me...He isn't a monopoly if there are other people doing videos...it's considered a oligopoly...lol sorry

[onewinged117]

@VantageX4 It would be a monopolistic competition sorry..

[q1hvc7r]

@patrickJMT

thanks for the help!

lol btw, u kinda sound like Will Forte from SNL... just sayin' :)

[poofterface]

I just wanted to say thank you so much for your videos. I often find myself staring at a problem for hours, not knowing at all where to start, then I'll watch maybe half of your video on the topic and instantly understand the entire topic perfectly.

I have no idea why your videos are so effective, but holy hell you're a good teacher.

[Hoz2001]

Thank you for not going painfully slow like some other people! *ahem khanacademy*

[NewTriShisAIDZ]

left handed FTW. thanks for all ur vids man, theyre great and have helped me get through math 1114 and calc 1205, u rock brah

[aestefyv]

actually, trybalnet06, length/ width can't be negative. So the answer would be only the square root of 1000.

[patrickJMT]

@trybalnet06 okie dokie!

[Noobsician]

@trybalnet06 Cool.... didn't know that distances could be negative.

[ANormalGuyGames]

@trybalnet06 True... but in this case we know that length x can't be -sqrt(1000), so I think it's completely AWESOME to leave the negative sign out.

The way you left the negative sign out was AWESOME, Patrick! I had never seen it done so awesomely!

Anyway... thanks for helping me study for my upcoming finals! :)

[abkmf]

@trybalnet06

There's no such thing as a negative distance :)

[Madeforviewing]

@trybalnet06

He can't have a negative perimeter....

[Madeforviewing]

@trybalnet06 He can't have a negative perimeter that wouldn't make sense. That's why the only critical number is the square root of one thousand.

[voetballeeuw]

@trybalnet06 technically that's right, but how is a negative x value going to work since it's for the rectangle. So that can be eliminated immediately.

[HeroFann]

Thanx for the vid my final is coming up soon!!!

@trybalnet06 In this case it must be positive cause there is no minus for width and height rite??

[splycedawg]

@HeroFann That is correct

[khawajacorp]

@trybalnet06 We are talking about a square here, no negative dimensions exist in physics

[Viggleik]

@trybalnet06 you are correct, but are the "MINUS square root of 1000" relevante to the question? no it isnt, but you should probably write it up, and the cross it out.... to prove that you now there are two solutions..

[RedAtenza]

@trybalnet06 As already mentioned negative 1000 is not pertinent to the question. You cannot have a width of -1000 meters.

[TanaiG1]

@trybalnet06 But he can't have a negative perimeter:| That wouldn't make sense...

[DeeJay0994]

@trybalnet06

length can't technically be negative, so i think you can take out the minus square root of one thousand

[nicgatornic]

@trybalnet06 no you are stupid... it cannot be plus or minus square root of one thousand because a length can not be negative. the square root of a thousand is around 31 and if it was negative then the length would be negative

[MrYousafBajwa]

Units

[absmaninga]

you could use the second derivative test to check if it is maximum or minimum

[bulldozerchn]

Thank you so much. I had absolutely no idea what was going on until this. THANK YOU THANK YOU THANK YOU

[gbalah162]

can you please help me. i HAVE AN EXAM ON THURSDAY!

I have a question that states; a box with a square base, rectangular sides and open top is to contain 12cubic feet of space. if the material for its base cost 3dollars/ft^2 and its sides cost 1dollars/ft^2, determine the dimensions of the box so that the cost of the material is a minimum. how do I derive the equation for this and my teacher has C=3x^2+4xy. how did she got that equation?

[FernzDaniel]

this is gonna sound weird but nice writing XD

[dadancinfool14]

Thank you, thank you, thank you!!!! You are a life saver!!! I am passing calculus because of you!!

[Charounson]

Patrick, this might be a bit off topic, but speaking of calculus, what is the integral of displacement?? That is, what is its application? What is it called in a real-world application?

[patrickJMT]

@Charounson that is a good question

[The12thAkatsuki]

@patrickJMT I'm not entirely sure, but the unit of that would be m.s right? (Meters times seconds). Does that have any physical definition?

[michalchik]

@Charounson For an integral to be meaningful, a variable (such as displacement ) must be changing. If you are talking about the integral of change in position with respect to time you are talking about the integral of speed which is path length. That is how far you travel along whatever path you follow, with respect to time.

[dexter127tep]

hi patrick you have help me improve my grade a lot with your videos and for that i thank you.

i was wondering if you could help me and my friends with this problem that we have been trying to solve for about a week but we can come out with the right answer.

*A large can of beans has a height of 15cm and a diameter of 10cm. Use differentials to estimate the amount of metal in the can if the top and bottom of the can are 0.05cm thick, and the side is 0.02 cm thick.

[patrickJMT]

@dexter127tep what kind of beans are in the can?

[The12thAkatsuki]

@Charounson The unit of that would be m.s (Meters times seconds). I don't think that has any definition. But I'm not entirely sure though.

[mcic1028]

your awesome....enough said

[shebby9]

thx man

[BSPDEMOTT]

Patrick>Even the best math teachers

[ParkUniversityACM]

Patrick, you are the best!

[patrickJMT]

@ParkUniversityACM glad u think so : )

[PeterBJams]

I have been struggling in my poorly organized, garbage First Year Engineering class, but thank God I have found a solution, Youtube learning!

[dagranmasta]

It's a bird, it's a plane, it's Superman, no it's PatrickJMT to save my calculus grade =D

[skrevat]

You're the friggin best. Im taking my last math course of my entire life and it's just getting so bad, and every time I have any problem i just type the topic and JMT and here you are. It must be gratifying to be able to help such a vast number of people. You're FANTASTIC!

[patrickJMT]

@skrevat yes it is nice to wake up each morning and to see lots of nice comments from people : )

[skrevat]

@patrickJMT you deserve it, you teach exceedingly well. I made an algebra mistake the yesterday and asked my professor if the way i did the problem was correct and he said "i'm pissed that you don't know how to the algebra for this." your technique is concise and you're a great person for doing this, really. especially free of charge because most of us are broke as a joke.