Calculus 1 Lecture 3.7: Optimization; Max/Min Application Problems

Calculus 1 Lecture 3.7: Optimization; Max/Min Application Problems

[@jjjjjokerface]

You're the first math professor I've ever seen who actually apologized for skipping a step in a problem. I wish all profs were like that!

[@Peter_1986]

He is the first math professor I have ever seen who genuinely cares about the students. This is obvious from his habit of constantly checking that the students follow all of his steps - you _only_ act that way when you actually _want_ to teach people something.

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@@Peter_1986 Yes..the only pain i get when i watch his video is not discovering him earlier

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Now if he would apologise for singing....just kidding!

[@hypersonic6649]

Agreed!

[@kylietacker5772]

I just want you to know that I sincerely appreciate you posting these lectures online. I love mathematics, it is just hard to see the concepts at times. You introduce and teach the topics in such a detailed way that I literally doubled my test scores after watching your videos. You have made such a difference, thank you. Thank you so much. -Kylie

[@Bitcoinminds]

Nice

[@whatislife142]

Double of 0 is still 0 honey

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@@whatislife142 LOL that’s a great one

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I want to thank you profesor leonard. I received my final grade on Calculus 1 and it was an A. I remember going to the counselor considering repeating the class, but I stayed and persevered watching your videos. I took class with one of the worst reviewed professors at my college and I am infinitely grateful that I found your channel. Now let’s conquer Calculus 2.

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How'd it go?

[@austin2150]

@@Bilbus7 He dropped out after taking calc 2

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I aspire to master calculus and someday teach it as well as this guy does, this man is brilliant. It's one thing to know how to do something, but to explain it in a manner that someone who is just starting out can grasp is an art! neither too much or too little detail, that is the key.

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I wish you good luck :)

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I just found your channel. I sat down and took notes while you talked like I would do in lecture. Difference is that you're significantly better at explaining than the math professors at one of the top Canadian universities that I go to.

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UW or UofT?

[@llawliet2310]

UW is like mid tier. Tops include of UoftT McGill, UofA, UBC, and Queens. UW is known for their pure mathematics programs at the graduate level.

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@@llawliet2310 bruh uofa could never even be close to being "top tier"

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@@magichorse18 uofa is ranked at number 4 overall officially and ranked number 1 for artificial intelligence in Canada, what are you even talking about? - And for mathematics, they are also among the top ranking for their research in algebra/ number theory. - Many reputable professors, like Don Page (who did his graduate work under Hawking) currently do research there - They are one of the few canadian universities that are partnered with large organizations like Google, CSIS and IBM. - They are also the only Canadian university with a division solely designed to study nanotech as well

[@brendanmurphy736]

Wonderful to be able to learn maths in my sixties. Great lectures Professor Leo.

[@umarrr174]

are you dead yet?

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Hope you are still alive and doing well.

[@kimjonguwu5659]

I am taking calc 1 in the summer, my teacher sucks at teaching it because he just puts up powerpoints, without your videos i wouldve failed 2 of my tests by now. Thank you

[@furkanaslantas8028]

You are the best Maths teacher that I have ever had. I am saying this because of your way of teaching. Most of the teachers especially professors are absolutely arrogant that they do not care whether their student have learned or not. You are a EXACT BIG BOSS...

[@noahbuck1636]

He is the only reason i am passing calculus... Thanks so much!

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+Noah Buck Same here

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lolz

[@RECTmetal]

I'm still failing by a little bit.. but him and nancypi are the only reasons why it's only a little bit and not completely failing lol.

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Thank you Jesus. Video from 5 years ago still helps me today!

[@Hi-bf7ec]

make that 6 lol.

[@cagedgandalf3472]

Thank you Leonard.

[@petroslazanis8466]

Ive watched so much of this series that I really wanna know what the classroom looks like behind the camera haha

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Same here lol, we’re invested now

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This teacher is hilarious and knows his stuff. You can really tell when someone loves what they do and when someone hates it.

[@mr.alfaromeo2350]

I might as well just skip math class and watch your videos instead, because I literally don't understand anything with my current math teacher, but I can easily follow your lectures 99.99% of the time. So just thanks for that man and keep doing what you do

[@chikanmao8326]

Facts

[@carloslaboy4279]

I completely ignore my calculus professor during class so that I learn things the right way, with professor Leonard, right off the bat. This man is the best and he deserves better lighting in that classroom.

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That's what i am saying best prof all time no bs HEEEE IS GREAT wish i knew him when i started calculus. But we live and we learn I am going to watch him for calc 2!

[@elyreyes1205]

when he apologizes for not explicitly showing the steps ''.'''

[@houkalani]

The beer can comments at ~1:13 made me laugh out loud. I love your sense of humor, Professor. Not only do you make math easy to understand, but you also make it fun as well. Endless thanks to you for taking the time to make this great resource available to everyone!

[@josephpryor5681]

I"m taking an online calc class at a community college and I was getting so frustrated with this section in the book. It looked like gibberish. I've watched a lot of these videos but this one takes the cake. You make it easy to get a first-class education without having to pay big bucks for a school with professors that don't teach with half this amount of detail. Thank you so much for everything professor Leonard!

[@dianetipps5078]

You actually make calculus more enjoyable, thank you so much for all the videos you post! Much appreciated.

[@Kar76060]

Sir, you are beyond amazing. I wish I was one of your students. With your clear and strict explanation, my math marks would reach the stars. 🙏

[@Xxjasminekaur]

I just want to say thank you for this video! I am from Australia and actually have 3 hour assessment today all on optimisation and functions in general with restricted domains. This is really helpful and gave me a very clear, and increased understanding. Thank you so much!

[@prestoloe]

My Calc 1 class in college is stuck online bc COVID-19 has closed campus. Our professor has directed us to you and I have to say... You are awesome in your teaching and easy proccess to help understand the concepts. Shoutout from myself and my class at University of Northwestern, St. Paul. Thank you for the awesome lectures, keep it up Prof.

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A prof who is v humble explain v slowly to a point of understanding with simple english

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I'm in AP Calcluas and this helped me with my homework so damn much

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Not all heroes wear capes. Thank you for being a great teacher.

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Professor You are the best math teacher I ever came across

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I feel like I leave a comment on every single one of his videos, but this man is responsible for me passing calculus.

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You are the only reason why I'm being able to learn calculus

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No one like you in this world professor, you are the champion.

[@aidenstumme]

The cardboard box problem came up in my homework 2 days after I watched this video. Was extremely helpful to come back to, thank you 🙏

[@gastrumkeee]

Professor Leonard, all the videos are much appreciated! They have helped me tremendously especially with Integrals. I definitely plan on watching your videos next semester for Calc 2. I respect the little things you do while teaching, for example, on this video from 44:12 - 44:24. Besides your math skills...Your off the cuff drawing skills are on point. Take Care.

[@MrHidden209]

Taking Calc 1 in the summer semester was one stupid idea. But thanks to you it is going well (:

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It's :) not (:

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+Nicolino Will omg really who cares its a smiley he can write it how he wants

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[@SantiagoRK96]

Yeah currently taking a 5-week calculus 1 summer class and after that a 5-week calculus 2 summer class. Pretty intensive... I don’t recommend it.

[@animeshmajumdar66]

@@SantiagoRK96 I have calc 1, calc 2 and calc 3 in the same semester 😑😑😑😑😑

[@Fermi_Consistency]

I greatly appreciate your work here. You have a significant talent for teaching! Better than all of my professors combined. I can learn more from 30 minutes of your videos than I would with 5 hours of class time. Thanks a lot !!!

[@adeltagash4096]

You just enlightened my soul.... those last 5 minutes answered all my questions thank you!

[@mmclaug907]

Thank you for uploading this! It really helps clear up some of the past problems I have had with Applied Optimization

[@cornelxbox25]

33:23 You could factor using AC method using -36x and -10x into (4(3x^2-36x-10x+120))=0. Also at 1:28:54 you could cross multiply since you have 2 ratios (left side is 4πr/1).

[@unknownloverr]

for that last example, the second derivative should be 4pi+4000/r^3

[@shep7484]

I AGREE. Jerry E. Shepherd

[@wilmdrdo1228]

watch until the end. he corrected it.

[@aliabrahimi3711]

For the second problem, anybody who has problem understanding it my suggestion would be, to take a piece of paper and cut the four sides and make a paper box. And maybe calculate whether you can fit more stuff in it that way or by guessing.

[@erickrivera4437]

Professor, your lectures are amazing! It is saving me for my final that I have tomorrow, thank you

[@nelsonrodriguez9974]

One of the best teachers ever thanks for helping me to pass....

[@sthandisomtetwa8637]

I use my varsity just to get the transcript, he is the reason why i love mathematics, keep posting we will subscribe

[@Red-bb6qj]

Man, that S" = 4pi - 6000/r^3 at 1:32:48 threw me off for a good while until I realized it was a mistake.

[@EstebanCanales-r8h]

I passed my Calculus course with an A (:

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"Doctor Strange aint got shit on me"

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oh nothing he just going hyperbolic

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This is so helpful, thank you for making these. Also 100% can't help but raise my raise my hand whenever you ask if your class gets it

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dude you rock this is life changing after having such a bad lecturing professor

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Thank you for posting these videos, I have been struggling in math and after watching this I feel like I have a better understanding of it :)

[@kolonyalanmaz]

1:11:22 the equation is not correct for checking x=0 because if x=0 then there will be no ocean pipe, thus the cost is gonna drop to half at the (x^2+25)^1/2 part(we need to divide this with 2 in this scenario). The actual minimum cost should be (8+5)/2=6,5 dollars. Correct me if I am wrong please.

[@jark7812]

7 years later after this video was posted, and im using it rn thx :)

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felt

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Thank you so much for your video's! Greetings from the Netherlands, Petra

[@afsanehtarhandeh7308]

Thank you so much. I am watching your calculus one to get ready for my summer classes and they are awesome. Defiantly going to watch calculus two and three lessons along with my next courses.

[@kepperan]

The opportunity for a really corny "one if by land, two if by sea" joke was missed here. Other than that, this is perfect and I love it. Thank you, Professor!!

[@arsal16]

This video concludes my prep for mid semester exam. Thankyou

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He makes math so much more enjoyable.

[@maksymandrzejdrzyzgiewicz5096]

YES! I was hoping you'd sing the quadratic formula song. Ah, brings a tear to my eye. It's like I've been in your class the entire time!

[@muhammadabdo2758]

sir , A BIG Thanks From EGYPT

[@saadwaheed5624]

In the last part , derivative of -2000r^-2 is 4000/r^3 not 6000

[@cagrioz9798]

When x is 0, the total distance via the land is 5 + 8 = 13, and the cost is $0.5, so in total, it should be 13*0.5 = 6.5, but if we place x as 0 to the formula, we're getting $9. it doesn't make sense.

[@beoptimistic5853]

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Amazing lecture. Definitely going to subscribe. Everything is so clear, and you make it fun to learn. Thanks!

[@afterall6418]

I am tired of watching your lectures professor Leonard. Thanks for your work.

[@tenzinjangchup4375]

we are not allowed calculators for these calculations in our class. its not fair T_T. Btw Professor Leonard, thank you for all these videos, they are really useful. I turn off Adblock when I'm on your channel :)

[@Siidhu47]

professor leonard, you sir are simply amazing at how you teach!!

[@beoptimistic5853]

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[@pubgplayer1720]

Great video! It was very well explained and i felt after watching that video i could confidently approach any optimization problem.

[@BijonNkhatu]

Best teacher ever

[@Mynhassty]

1:18:00 The textbook didn't show where the formula came from. This is why I supplement the reading with your classes. Thank you!

[@beoptimistic5853]

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Being ripped and smart, that's what I wanna be. Teach me how to get ripped.

[@kimvangvideomarketerbangko3265]

In the beginning I was like fuck yeah, finally a framework on how to think in order to get word problems like these into numbers and variables, and then how to reduce your formula to one variable. After watching the whole video, it has all been reduced back to wizardry for me.

[@karimjiwa9279]

I get 4000/x^3 as the 2nd part of the 2nd derivative. Can you please explain how you get to 6000/x^3?

[@AndrewDzula]

It was just a small error, I checked with a derivative calculator; it is 4000/x^3.

[@hortonhearsaworld3137]

FINALLY, BLESS YOU?! THESE VIDEOS SAVED ME 🙌 SO BLESS YOU SIR

[@simonbongani8099]

you're the best!!!!!!! you help me every now and again........thank you very much

[@archangel1309]

Shouldn’t the second derivative at the end be 4pi + 4000/r^3 instead of 6,000? Edit: I seen the ending he fixed it😂

[@juliawojtowicz8773]

This was such a helpful and informational video! Thank you!

[@SD-nw8ch]

These are awesome series. Thanks for spreading the knowledge. I am confused on the Pipeline problem. The minimum cost, if we go completely over the land comes to $6.5. [(8+13)/0.5]. What I am missing? I feel the formula taken for undersea part need to be modified as if we put 0 for X, it gives $5 as cost rather than $2.5. May be the cost of undersea also needs to have X as multiplicative factor.

[@NJdevils47]

OMG IT FINALLY ALL MAKES SENSE! Thank you so much!

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I wish you were my teacher

[@mariotraina3186]

Anyone get the final answer for the second example with the volume of the box? After plugging in 10/3 is the answer 217 7/9 in^3 for the volume?

[@beoptimistic5853]

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[@mgibson323]

at 38:35 answer is actually 19600/27, not 726. But I'm sure you already know that :-)

[@beoptimistic5853]

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[@quixiee_]

Awesome video, thanks for the help 🙏

[@michaelgeinopolos6911]

Factoring v'(x)= 4(3x-10) (x-12) instead of using quadratic formula.

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He is such a good teacher damn.

[@Apolorock11]

32:10 😹 That's why I come here to learn

[@dannylo5875]

I don't understand how problems can be so different yet the homework is so easy...like if it would throw you off... how to react to this.

[@feezyfutruck6084]

Learning how to lay pipe from the guru himself

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You are just awesome . Looking forward for more videos from you

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Dude. Prof. Leonard grew up on a dairy? He really is Clark Kent!

[@Tyler171able]

Thanks I had the otter version of this type of problem but was able to complete it

[@tjmartin8261]

for the second example I plugged 10/3 into V= x(30-2x)(16-2x) and got 19600/27 not 726. Did he mean to say plug 10/3 into the simplified version of the original(after distribution)?

[@ZaUkSsKuAz]

Professor. If you look around the hour mark of this video, we take C'. I missed what happened to the 4 when going from C'=1/2 (x^2 + 25)^(-1/2) + 4 - (1/2)x to the next step. Hope this question makes sense.

[@zb4358]

the 4 is a constant. the derivative of a constant is always 0. since 0 does not change anything, he didn't write + 0 in the equation for the derivative

[@victormavika9168]

he is good!!! where can we get more videos of calc 2 and 3. i like the prof who writes on board than the one the ones who thinks using slides is the modern way.

[@ahmetayyildiz9549]

I think on the oil problem there is a mistake.If we go all way on land it takes 13 km and the cost of this way makes 6.5 $.This is cheaper I guess.

[@JuniorOrtiz738]

Do you have a video on Newton's method professor?

[@andrewchan7927]

Hi Professor, thanks you so much for the video!!! But, i got one question. How do you know the minimum surface area of a can is a relative min or absolute min?

[@pashafn3171]

tank you sir

[@maksymandrzejdrzyzgiewicz5096]

37:28 *500 thousand people, simultaneously:* WE WISHN'T

[@philipohara1009]

Note. 8 as a distance would give a cost of $13. Not sure how 9.43 was derived

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Such a lifesaver. Thanks!

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These lectures are so helpful! ❤️

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is this course emulating the book on calculus by Ron Larson and Bruce Edwards? the playlist has the same structure...

[@IceTactics]

Calculus is awesome.

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Prof. You are the best