Optimization Problem #2

[47der]

@patrickJMT the best part of this video (besides the fact that the material is much easier to follow than in class) is that i can rewind it if i don't comprehend the concept the first time as opposed to raising my hand and disrupting the flow of the class every few minutes. Thanks alot for taking the time to post these, math guru!

[patrickJMT]

@47der yes, rewinding is a good thing :)

[Givemeasnickers]

Lefty's are smarter then rightys! Right brain power!!!

[soccer4ever799]

what if you take the first derivative and your critical value is 8. Then once you plug it into the original y equation, it gives you 0...this is for another problem btw, same procedure, idfferent numbers

[BYAZIT]

it's helps a lot... thanxs

[MIThopeful]

Awesome videos!

[lilythatgirl]

I promised myself I would thank you (yet again) if I got an awesome FINAL grade in my calc class!! .... And guess what, I did!! I THANK YOU from the bottom of my heart because it was your videos which truly helped me more than my professor ever did!!! :D THANK YOU PATRICKJMT!! I look forward to using your statistics videos on your website!

[YellowAsphalt]

Ugh, when you put an exclamation point after "Derivative" its like a light bulb going off in my head

[amandwee]

So what if they ask you for the min instead?

[denidzoja]

are you a professor or teacher somewhere? Just curious. Because you're incredibly helpful

[metalmine1]

I want you to teach at ALL the universities simultaneously. That way, no one will ever complain

[patrickJMT]

@metalmine1 oh, people would still complain

[gloopybuger108]

@patrickJMT No they won't. Hey, what the heck Patrick...your hand is taking up all the camera space! Geeeeez.

[xIChromeIx]

is it possible to do this using lagrange multipliers?

[o0xHorizoNx0o]

Why didn't I come here SOONER!??!! THANKS!

[Axsolrox]

Lol "next time: dont watch" I love you Patrick :D you make Calculus feel like the best subject ever :D Im definitely using you in college lol

[jojogirl2008]

thanks so much! 

[durrthock]

lol, this exact problem was on our exam review sheet, I wonder if the person that wrote the sheet watched this?

[theLyricsSuck621]

Why can't you set x as the whole length of the rectangle? Why does it have to be half the length?

[durrthock]

@theLyricsSuck621 You can, its just going to be much more complicated that way.



[theLyricsSuck621]

@durrthock Got it.

[dritch11]

thanks for your videos man really helpful. i wish u were my personal tutor for calculus

[CyberViewer007]

I have a problem similar to this but I have to use a trapezoid where the base is the diameter. Can you give me any tips to start it?

[ICarnag3I]

I feel as if this is the hardest topic in calc

[TheJewel121]

I am a straight guy but I would marry you for your awesome math skills alone.

[bharathsf]

When I substituted values until root of 8/3 in the derivative, the values just keep on decreasing..I am not seeing that the values increase until x=root of 8/3 and decrease after x=root of 8/3...Please help...from your previous videos I learnt that the values will be increasing or +ve or-ve until the critical number and -ve or positive after the critical number which will help us decide if its a local max or min

[bharathsf]

@bharathsf OOps I wascalculating it wrong...sorry.... anyway Thanks a lot Patrick....I am preparing for my exams in feb 2012 and I am brushing up my basics of the last 12 years..Your videos are like a blessing...Pity I didnt have these videos when I was in school...

[tina0595]

oh my god thank you



[Mike3138]

if you had to put this in an economic context.. what would you say the square could represent?

[Leninade]

can you take the second derivative to determine that its a max?

[patrickJMT]

@Leninade you can use the second derivative test, yes.

[junior1984able]

Nrxt time post the problem on the board.

[patrickJMT]

@junior1984able next time: dont watch

[GenuineBorownBoi]

@patrickJMT That patrick, was badass

[FXrubiP]

I love you man

[CPPA]

could you have taken the second derivative to determine concavity, and therefore whether or not the point is at a max or min?

[SuperPeacelovemusic]

I decided to look at this 2 hours before my test although we've never done a problem like it in class before....I just wanted to understand the concept & guess what a problem like this was on my test, YES, thank you.

[SuperPeacelovemusic]

"What the heck are they saying"....my thoughts every single time.

[TheNumber2Pencil546]

"heres my shameless plug for my website" haha love it

[MsHoneyBBQ]

i wish u taught physics like this too! ...... wait.... go to school and learn physics real quick then come back and make killer vids for me ;P

[MultiMoe91]

whats your email?

[ahmedalsharman]

good video, can do more examples in non linear optimisation and Dynamic optimisation

thanks alot

[DarthYoungling]

I'm wondering why I thought this was so hard.. :) Every time I watch your videos I realize this stuff isn't hard at all.

[patrickJMT]

@DarthYoungling perfect, that means i have super powers ; )

[NothingSpecialMusic1]

@patrickJMT Seriously dude., You're helping me out so much for my final tommorow.

[helenblanche]

i got perfect on my first calc test thanks to you!!! keep up the great work! these videos really do help :)

[ClayPigeonKiller]

Do you do college level chemistry too?

Keep up the good work.

[uni4life1619]

You helped so much man! I wish you were my math teacher, you explain things in such a clear and organized manner, keep up the AMAZING work!

[guperan123]

LOL@0:40 eat minus x squared

[mustafamufasa]

this is much better than just having to read the book. it sucks not having someone teach you the material.

[magicsuyi]

Thanks a mill man, best math prof online

[e13e7]

LEFTY!

[Geek4Lif1]

fuck! This was on my math final today and i couldn't do it :(

[MrONEMILLIONCOWS]

feels like im watching porn for my brain O.o....

[patrickJMT]

@MrONEMILLIONCOWS that would be a good advertising technique. no one wants 'math videos' but many would accept watching 'porn for the brain'

[lpperalta1]

@patrickJMT So my girlfrined allows me now to watch porn ;D

[dsignator]

My calculus teacher should just play your videos instead of teaching us and life would be easier.

[samgam2]

Thank you so much!! you saved me on my final! I love you!!

[charminator123456]

So I see your wedding ring is gone... ;)

[patrickJMT]

@charminator123456 no, it is there

[10n3r]

@patrickJMT lol that was creepy!

Glad everything is going well for you Patrick, and thank you for these videos!

[iviriya]

thanks a lot. I'm your fan. You are my rescuer. Thankssss

[srslayerz]

haha awesome, i was doing this exact problem when i felt like checking your vids.. BAM PatrickJMT saves my day.

[patrickJMT]

@srslayerz i am waiting for someone to get a tattoo of my face on them... $500 to that person

[srslayerz]

@patrickJMT how about you give me the mathematical part of your brain instead of that $500.. ;)

[maxazria11]

@patrickJMT if only we could see your face

[dhaval712]

@patrickJMT but we never see your face. :p

[jetv42]

I wanna make love to you after watching this video.

[thelegendz]

You are so helpful! Thanks!

[soloryder711]

Great video. You have made this much more simple to understand than how my teacher explains it.

[china2207]

so where would u plug in the square root of 8/3 o check if its a maximum or a minimum? by the way u explain so well.

[patrickJMT]

@china2207 u could show that the derivative is negative or positive by taking a number less than sqrt(8/3) to show the function is decreasing or increasing and a number larger than sqrt(8/3) to show it is increasing or decreasing to justify you have a min or max

[krndude7777777]

@china2207 you can plug into 2nd derivitive, if its negaitve, its a max, positive is a min

[dagranmasta]

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

[dagranmasta]

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

[romyboy]

is you answer is in area or in dimension im lil bit confuse i the thought D=2x+2y why is it in D=2xy plz help im confuse

[hotsum0ta]

Thank you so much for these videos! They have helped a bunch :D

[LMT9067]

You have helped me so much as I have been going through the courses to get my math minor and engineering degree. Do you have any videos for partial differential equations? its the last math class I will ever have to take :(

[smokingun7]

thx a lot!

[orioles9461]

can you do harder ones please? these are good but my tests have harder stuff than this.

[jonolollmao]

is it true if you plug in x for the second deriviative and its >0 then its a minumum point and vice versa? but what about point on inflexion ( =0 ), this confused me

[Tobey7049]

thank you thank you thank you x infinity!

[gsharpshooter80]

thanx man but i still suck at this i think im not looking at it the way everyone else is ohh well heh.

[O0oSorousho0O]

@gsharpshooter80 Same. Watch it again you'll get it. I zoned off a lil'.

[gsharpshooter80]

@O0oSorousho0O i'll try !

[rodthelumor]

Great work Man.. big Ups to you... you work is definitely most diligent and respectable!

[Manbearpig8900]

you rock!

[donreychronic]

patrick man i love you.

[flaco954]

The x there is actually just the multiplication symbol.

[Lucildor]

@suckmythach That x he wrote there is just a multiplication sign. I know its confusing, I thought the same thing at first! :)

[mambofatale]

Thank you so much for the patient explanation! I struggled with this problem for 2 days before I watched your video and I finally understood! Doing online calculus is tough, and you really help to give the feeling of sitting in a classroom when it really counts. Thanks again!

[vallakan]

tnx mr LEFTY

[LBnation30]

You are helping me so much. Keep up the great work man.

[Jesuskrieger]

Oh I coulda sworn u said to find area...oops haha. I did get the dimensions, but I went on to find area. Would it be (64sqrt(6))/9 ?

[raghmar]

Thanks dude. Great stuff!!

[jdawesallen]

You are super helpful!!! Thanks!!!!

[JzzdInMyPant]

you explain this so well i feel like i am cheating :D

[Lunchsacks]

this is #24 in the "single Variables calculus" 6th Edition. chapter 4.7

[Thecowofwar]

that was great 4:47 theres no way in he... theres no way about it

[elementoxygen]

I love every single one of your vids, which help me a lot in math (that is my favorite subject to do)!

Yay for patrickJMT helping me in Calculus, and everybody else : )

[coolkid19901]

Nice vid, you might want to use an asterisk symbol for your multiplication sign because it really looks like an x! Good Job, Keep it up!

[rocknrollerguy37]

x being arbitrarily close to 0 would make a very narrow, tall rectangle, not a short wide one.

Other than that, great videos and I love the rest. Lots of help man, good job!

[patrickJMT]

i was laying on my side when i was thinking about it...

[Hallucisquid]

@patrickJMT You're funny =D

[manoj0072006]

what is your email address?

[avzey9]

good job dude

[abaraimido]

God Bless you Man!!

[Chicababe907]

OMG! I saw this video last night, (a night before my test), and I swear to you my professor put the exact same problem on the exam except with different numbers! thanks to you I was able to do it without a problem!!! I know you must hear this all of the time but you help more than you know!!!!!

[grreat2]

IB LOL

[bharathsf]

@Chicababe907 Once you see this video and solve a couple of problems you wont forget for years unlike college professors classes where you most probably will be dozing off in the last bench:)

[southoreast]

Yes. I'm definitely interested in viewing your video concerning the application of the second derivative test to find max/min values. I would appreciate that greatly. On a more personal note, what would you say to an individual like myself who aspires to obtain a B.S. in math who also has a questionable strength in his foundation( algebra,etc). My foundaton in math can be compared to a removable and jump discontinuous function, too many gaps and holes,lol.

[patrickJMT]

everyone 'relearns' algebra as they go.

my suggestion would be to brush up on it over the summer know.

know basic graphs, how to solve a variety of equations involving a variety of functions

[southoreast]

Patrick, you are the man, seriously. You proved that being aware of max/min values, increasing/decreasing test, first,second derivative test all helps. However, i have a question. Is there any way to use the concept of the concavity test in optimization problems and if so, could you possibly demonstrate one that involves such? Once again,you are the man. I definitely will be contributing to your site in the form of a donation.

[patrickJMT]

yes, you can use the second derivative test to determine if a critical number is a local max/min value (in most cases)

[patrickJMT]

i have a video on using the second derivative test to find max/mins if u are interested

[DEATHBUGGY]

your videos pretty much ensured that i will go to university...cant thank you enough!

[patrickJMT]

that is why i am here : )

[deathbystar]

You've helped me understand optimization with ease!!! not like others, even my own professor! who make it too complicated! THANK U!

[333329753]

how do we know the parabola is upside down :P

sorry for the dumd question

[patrickJMT]

if the coefficient on the x^2 term is negative, for example:

-x^2, -4x^2 + 7x - 49, -10x^2 + 8x, etc.,

the parabola opens downwards!

[faisalfw123]

great thank you

[dontcallmedarling]

I have a math final today and this helped me emmensly!!! Thank you so much!

[Jechux1106]

how did u get ur area 2xy??

[choochiu]

The product of xy is the area of only one rectangle.

So 2xy would be the area of both.

[patrickJMT]

yep! thanks for helping choo!

[Awsomedotcom]

he should have labeled the left side as x as well but he didnt

[cosm0]

Excellent tutorial my friend, best subscription i ever made :]

[patrickJMT]

ha, thanks! : )

[jeger05jeger]

why cant you just call the hole thing x insted

of 2x.

Thanks for a good explanation btw.

[vietchicken]

Thanks so much! I'm studying for my exam and this problem showed up... with different numbers. :D

[smckenna162]

Way better explanation than how my teacher does it. Thanks for the help

[BigT4313]

Kind of a stupid question, but when you look at any optimization problem, just to get started, what should be the very first thing you should look at or try to figure out?

[patrickJMT]

well, understanding the problem first is the key! then i would draw a diagram. the hardest part (to me) is trying to find the equation that you need to maximize or minimize; this is often the part where you have to be resourceful!

[crackdadd3]

you need a equation y = x , this one was easy cause they gave it to you, you plug this into the problem your are trying to find

[nanohark]

OMG, finally a good math teacher! My teacher comes late every time for a 50 minutse class, leaves 5 mins early and only explains the theory. You have saved me! I will drink your knowledge and leave you DRY! MUAHAHAHAHAHA!

For real, thx.

[patrickJMT]

sorry your teacher is not the best!

i am happy that ! could save you!!

[TheFallOfGirl]

You are the best, thank you so much

[patrickJMT]

no problem

[Fdpelison]

by far, the clearest anyone has ever explained math to me. you are my hero.

[patrickJMT]

nice! : )

ahhhh the comments... like a wave of happiness at the end of a long day. : )

glad i was able to help

[cmm4fd]

Wow thank you so much for posting these videos. You have just made me understand all of my optimization problems 10 times better than my professor.

[patrickJMT]

happy that i could help!

[RussianCosmonauts]

Without you I would be failing. Went from like a 65 to an 80 with your help after viewing your videos for just a month, which is a lot for AP Calc. Hopefully I can make it into the high 80's, maybe even the 90's this marking period :)

[patrickJMT]

good luck in your class : )

[patrickJMT]

i am trying!

[The6ChickMagnet]

More More More :)

[Tonyk23]

Correct me if I'm wrong, but isn't the equation supposed to be:

A = 2(xy)

and not

A = 2xy ?

Or does it not matter?

[patrickJMT]

2(xy) = 2xy

[Garee1980]

You video is helping me learn Calculus a lot smoother! You should post more videos, you really know how to explain the different concepts in an understandable way.

[xroyaldevilx]

Thanks for the video. You should make more, thanks!

[patrickJMT]

glad it helps! you are VW!

[Yuudai]

PLEASE POST MORE! TY VERY MUCH!