Max and Min and Second Derivative

Рет қаралды 257,670

Күн бұрын

At the top and bottom of a curve (Max and Min), the slope is zero. The "second derivative" shows whether the curve is bending down or up. Here is a real-world example of a minimum problem:
What route from home to work takes the shortest time?
View the complete course at: ocw.mit.edu/highlights-of-calc...
Chapters
00:00 Outline
00:24 The Second Derivative: The derivative of the derivative
01:43 Examples of Second Derivatives
08:00 Convex and Concave Curves
09:28 Locating the Maximum and Minimum and the Inflection Point
23:40 Application: Driving to Work, Finding the Minimum Time
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
Subtitles are provided through the generous assistance of Jimmy Ren.

Пікірлер: 194

@tomscik1965 8 жыл бұрын

MIT courses are not about teaching simple things in a complicated way which ordinary ppl do not understand. It is about teaching complicated things in a simple way where ppl get an extra 'dimension' of understanding. THank you Sir for an excellent lecture and thanks to MIT initiative to provide these courses online for rest of the world.

@gurleenkaur9601 6 жыл бұрын

Tomsci K very true.

@111smily111 4 жыл бұрын

I got really emotional seeing Professor Strang talk. Seeing a person devoting a lifetime to math and teaching itself is touching and inspiring.

@lewis6825 Жыл бұрын

I have had the same reaction, actually. Btw he just recently retired at age 88. End of an era.

@mayurkulkarni755 7 жыл бұрын

34:02 "Drive at a 30 degrees, hope there's a road going that way. Sorry about that point" LOL this guy is genius and funny at the same time :D

@nishantshankarkhan4879 5 жыл бұрын

This is called a genius because I don't know about others but this presentation is massive and therefore you are the teacher of MIT.Thanks a lot.

@ajayupy 4 жыл бұрын

It's like watching a superhero of calculus at it's best. Thank you, Sir!

@Venturebits 3 жыл бұрын

Amazing how Professor Gilbert can explain the key ideas clearly. He is by far the best teacher I ever had. A lot of the concepts he explain I usually learned them by memory now I can see the big picture.

@Tzvetkov 6 жыл бұрын

"And there's a sign of hope. It started bending up."

@Hiyrustrider 11 жыл бұрын

This wasn't even part of what I was looking for but I watched the whole thing, I enjoyed this lecture because he's a great Prof.

@saiprakashhadnoor3987 4 жыл бұрын

No words for this man's teaching.Really loved it.

@NothingMaster 5 жыл бұрын

Strange truly deserves a Medal of Honor of sorts for his monumental contributions to the advancement and dissemination of mathematical knowledge and intuitions in these MIT series. The Internet has created a whole new and accessible dimension of learning not available to the previous generations of students.

@sajidalishah2653 4 жыл бұрын

No Matter what Technology advances, need of such brilliant teachers will always be felt

@ingeborgsvensson4896 6 жыл бұрын

I wish I had had a teacher like Strang in high school. The example of the way to drive to MIT are great ways to explain why you would use these derivatives in real life. Great course! Thank you.

@vinodsah8330 4 жыл бұрын

What a teaching style

@aryaanpetiwalla2655 3 жыл бұрын

I saw concave and convex curves, and thought this lecture might be too difficult for me. Then, he explained it so easily and well, and I’m very satisfied having watched this. Thanks a lot!

@georgesadler7830 3 жыл бұрын

DR. Strang thank you for another excellent lecture on classical selection of max and min problems in calculus.

@saisaske1 4 жыл бұрын

The maxima of "like" function for this video is infinte. This video kept on giving me "aww" moments. Thankyou sir. I always wondered why we need to take the derivative of x and assign to 0. I will always be indebted to you.

@ninomatcharashvili9739 6 жыл бұрын

I have been studying from you sir the main topics in calculus, thank you!

@silkieshag9703 6 жыл бұрын

excellent explanation, you could be in a regular university, but you could watch classes from the best teachers in the world. Thanks MIT

@nashabusmani3220 5 жыл бұрын

Most beautiful way to define double derivative test. Hats off to you sir.

@laldinpuiarenthlei7615 7 жыл бұрын

hats off for gilbert strang

@abdalrahmanshaddow6121 4 жыл бұрын

this man play beautiful mathematical music , the exact definition of deep learning

@LuisMunozCompScience 12 жыл бұрын

Thanks. One of the most simple, and brilliant explanations regarding this subject.

@zarsblackhorse123 5 жыл бұрын

I never thought i could finish this 38mins video lecture. but once i started to watch its really hard to close the video. Thank you for this excellent lecture Sir and also thanks to MIT for this initiative.

@Zwide97122 Жыл бұрын

Doing my masters in Econ Science and I still come to watch these intuition classes by Prof Gilbert. Legendary!

@zyxwvutsrqponmlk2000 13 жыл бұрын

This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus after viewing the three parts of this vedio series. Thanks to you. To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too. A BIG THANK YOU!

@2fluffybunnies 11 жыл бұрын

Holy cow, 38 minutes with you on KZfaq did more good then 2 hours with the book. THANK YOU SO MUCH

@maelena14 13 жыл бұрын

God bless you Mr. Strang!! Thank you very much for your efforts... I am taking a second look at calculus as I prepare for graduate school and your videos have been most helpful! Thank you!!!!!!!

@solvability2782 2 жыл бұрын

Thank you, professor. This is amazingly clear.

@nemanihanumantharao7439 6 жыл бұрын

the greatest calculus teacher in the whole wide world

@Amine-gz7gq 18 күн бұрын

This video/topic is important to understand the Laplacian in multivariable calculus

@Oneeightseven6 6 жыл бұрын

This man, has explained this very well!! Thank you for this video!!

@TheFirstBK 11 жыл бұрын

Thank you very much Dr. Strang, wish I had you back when I took calculus.

@zyxwvutsrqponmlk2000 13 жыл бұрын

This is a Hats off to the Calculus Master. Durring my engineering this was just a night mare. I now love calculus. Thanks to you. To increase the reach to remotest areas of the world there are lots of breakages that happen during the sessions. It would be good if these vedios could be available for lower bandwidth connections too. A BIG THANK YOU!

@skoolwal3874 9 жыл бұрын

Excellence and hard work personified!!

@zensorrow1 11 жыл бұрын

"Why move myself 20 miles to MIT when I can, with a click of the mouse, move not 20 inches and absorb the same knowledge." ~The wise musings of an unemployed student drowning in debt

@oskarrask9413 4 жыл бұрын

how did it go?

@renaeneufeld 7 жыл бұрын

Thank you for this video!! Very well done. I understand soooo much better.

@micahbrill 10 жыл бұрын

I really enjoy your videos. You're helping me through my Business Calculus class at Brockport College this semester.

@laurenmarzlock3419 7 жыл бұрын

I love calculus, It is great exercise for the brain. I love the logic and the patterns.

@FordBurden 12 жыл бұрын

Thank you! I am doing a condensed 8 week course that is kicking my ass and this is making it all "tangible"!

@KarlSmithByrne 12 жыл бұрын

'If I knew where we were (22:58) mathematics would even more useful than it is...which would be hard to do!' This guy is fantastic.

@kglayyet 11 жыл бұрын

Thank you so much for uploading these courses..

@mj6637 7 жыл бұрын

Great work, Professor!

@nandakumarcheiro 2 ай бұрын

The first and second derivative as combination of zero positive and negative bending as it oscillstes between convex and concave planes differentiated by that an be applied in digital communication developed by Nyquist further developed by shannon where the basic first and second derivative as otherwise may be a function of basic digital functions. Inspired by MIT course offered by this professor. Sankaravelayudhan Nandakumar

@ankushpatil9039 6 жыл бұрын

I can't resist to myself to watch these explanations.

@pettyjames7 8 жыл бұрын

Thank you, great job explaining.

@MISERSTYLE 11 жыл бұрын

This guy is an amazing teacher.

@jrmom4u 5 жыл бұрын

Appreciated with impressive lecture!

@erikandresgarciavillarroel3005 6 жыл бұрын

Thanks a lot for sharing your knowledge!

@sanjeevmadan2610 4 жыл бұрын

Many thanks, you are excellent, so simple so clear

@alias40anon 6 жыл бұрын

Very good point to point explanation

@shibsankarbera9218 8 жыл бұрын

nice lecture ...really I highly influenced ....because of its simplicity and graphical interpretation......

@mohfa1806 8 жыл бұрын

Sorry i should have watched the last 40 seconds to know the answer to my silly question now :)..the answer is there....great video and wonderful lecturer

@arjunch2755 4 жыл бұрын

this videos are enough for gate exam without practice,i love this lectures

@nandakumarcheiro 2 ай бұрын

The triangulated surface in modili form is derived at in between maxima and minima around the point of inflection in between with increase in frequency of transition as applicable entropy equation in understanding the hydrogen attraction and repulsion in boson gas as a function of interactive magneticfield over electricfield as Hall's interpretation. A definition on electron gap in between atom and nucleus could be arrived at the interpretation of first derivative and sevond derivative based on the sign of the sevond derivative Sankarabrlayudhan Nandakumar.

@Doug19752533 8 жыл бұрын

Prof Strang is COOL! love the videos

@choungyoungjae8271 7 жыл бұрын

thanks for graphical explanation.

@andreranulfo-dev8607 Ай бұрын

Pure gold!

@nandakumarcheiro 2 жыл бұрын

The oscillation becoming bending down convex and bending down a concave with inflexion point at which the sign of bending oscillate between concave and convex producing positive and negative energy.

@tyrokell1 11 жыл бұрын

you are brilliant! thanks a lot mate

@thebaniyabox8147 12 жыл бұрын

if i could afford the mit's fees i definitely would have been a part of that institute which is the best in the world.

@nandakumarcheiro 2 ай бұрын

The conflection points becomes the square comfogurstoon points pave the way for basic figitsl numbers while denfing the pulses in between zeros and ones in signal sending in computstionsl digitsal mathematics.

@lauras.9757 6 жыл бұрын

Great lecture Prof - thank you! Thanks MIT!! I love me some ♡Calculus♡

@lauras.9757 6 жыл бұрын

I have now attended Walter Lewin's Physicd class, Susskind at Stanford and Yale Physics and now Mathematics at MIT! I am thrilled to learn from the greatest lecturers/ professors of the day - this is an opportunity I would not have otherwise and it means everything to me. I've learned so much! My sincerest gratitude to you all for these lessons.

@qzorn4440 6 жыл бұрын

what's up doc? a very relaxing informative lecture. thanks. B+)

@AnkushSingh-kj1zl 6 жыл бұрын

Nice lecture 👍👍👍

@Khwartz 7 жыл бұрын

Really Very Nice Smooth Teaching :) Btw, been French, looks to me that the French name for calculus is way much meaningful as it is "analyse" (analysis), which is about "cutting in (little) peaces" etymologically, which goes very well imho with the concepts of "dx" and "dy" :)

@eleonoraformatoneeszczepan8807 3 жыл бұрын

MIT OpenCourseWare Max and Min and Second Derivative 'Professor Strang Chapters. The Second Derivative: The derivative of the derivative. Subtitles: Jimmy Ren.' 2:10 min ... acceleration 2:56 min ... Newton's Law, F = ma

@ghanshyammishra5297 7 жыл бұрын

best explanation

@kaventhwe 11 жыл бұрын

this stuff helps thanks

@neilchakr 3 жыл бұрын

how. do. you. explain. so. well.

@nandakumarcheiro 2 жыл бұрын

The combustion graph follow a sin and cos curve follow maximum and minimum.

@yuzheng3091 11 жыл бұрын

thank you so much!

@user-ny1vt3ek4i 7 жыл бұрын

Thank you!!

@nandakumarcheiro 2 жыл бұрын

Thus maxima and minima points with combustion inflexions follow a sine curve and cos curve.

@Joe11Blue 7 жыл бұрын

The good Dr. needs to switch to de-caf. Excellent presentation.

@storaman12 13 жыл бұрын

Thank you

@elamvaluthis7268 3 жыл бұрын

Very nice explanation.superb.minutest of minutest study is knowledge.h ow?how?every thing is from mind.Mind is full of equation.while going to bed you must shake your head violently then only equations shall fall down you will get sleep.

@MsManoodle 10 жыл бұрын

this guy is great!

@santoryu8940 7 жыл бұрын

hi youre cute

@SydiusVideo Жыл бұрын

Thank You!

@gdogvibes1 11 жыл бұрын

Thanks.

@gaithouri 13 жыл бұрын

thank you

@allenk7635 6 жыл бұрын

Thanks!

@horizonbrave1533 5 жыл бұрын

@ 8:56 spoken like a true Mathematician!

@chancewatkins5071 7 жыл бұрын

Love this, I've subscribed. Thanks for sharing; Jesus Christ Bless

@LenaIvanovak 12 жыл бұрын

great! Thank you!)

@PabstOut 11 жыл бұрын

divide x on both sides (3x^2)/x=(2x)/x, then simplify to get 3x=2, then divide each side by three to solve for x, x=2/3

@mahmoudeldesokey147 6 жыл бұрын

The best👌

@LAnonHubbard 12 жыл бұрын

Thanks Professor Strang.

@user-qj4zr1pj9y 2 жыл бұрын

Do you stil remember what you have learned from these lectures ? 😄

@newbarker523 2 жыл бұрын

@@user-qj4zr1pj9y Hi. I was the original poster (though have a different account now). Yes, I still remember what the lectures taught me. Probably because I have found it useful in my job. Maths (I'm from UK) is awesome!

@user-qj4zr1pj9y 2 жыл бұрын

@@newbarker523 Good for you !! Yaa Maths is awesome when you learn from Gilbert.!!

@FallenSparrowNz 11 жыл бұрын

you can only do that if the formula for the equation is in the form ax^2 +bx = 0 in this form we can presume that one anwer has to be zero, and it is simple algebra to find out the second number. You would have not seen this very often because most equations we work with are in the form ax^2 + bx + c = 0 this c value muddles it up and means you can not do what he did.

@HypnotizeCampPosse 11 жыл бұрын

No kidding, it looks like the biggest problem with getting a good professor is getting one that's not arrogant, presents the facts in a logical way and the best professors will incidentally get you to use the best practices without even having to stress it.

@taimoor722 12 жыл бұрын

thanks u sooooooooooooo much

@mohfa1806 8 жыл бұрын

Thank you for this video......just a question , in the end problem why we assume that the answer is the minimum time and not the max time?.....any suggestions?

@surajyergude 5 жыл бұрын

Will you help me how did you get to the 30 degrees?

@lowersaxon 5 жыл бұрын

First class teacher.

@changtillend5718 3 жыл бұрын

Grate...

@jayadrathas169 9 жыл бұрын

Good one bruh..was a bit skeptic at first due to,too much fidgeting of yours...but the last problem was cool

@donaldmaase776 9 жыл бұрын

Interesting he talks about inflection point in the US economy in 2010 and thinks we might be turning around (as an example).......it has now happened...........:-)

@lauras.9757 6 жыл бұрын

Check out the Elliot Wave Theory to see some beautiful market behaviour analysis and predictions. Calculus, fractals, wave theory... sexy stuff. :)

@MATHSOLVESZONE 5 жыл бұрын

Awesome video!!!!! #mathsolveszone #maximaandminima

@yixiaohuang4148 2 жыл бұрын

Great example, but If the b was to be smaller than x then there should be an "absolute value sign" on the right side, because one cannot lessen the time by driving backwards, right?🙂 But this wouldn't matter since it always take longer to overshoot and drive back.

@JanBuatim 14 жыл бұрын

i could say the same as zik667, my teacher had a post doctor at a french institution at math teaching and still hadnot that good didactics. MIT rules, i wish i could study over there. Im brazilian and i have my engineer course at UFSC - Santa Catarina Brazil

@AndyThomasStaff 7 жыл бұрын

I'm having trouble understanding the word problem at 26:27. I don't understand *why* the fastest time is where the first derivative of the graph is zero. What is the actual graph, and why does the derivative of zero (where the first graph's slope is zero?) mean the fastest time when solving the equation?

@faliakuna8162 7 жыл бұрын

It is because the function "time it takes to arrive at work" reaches either a min or a max point when its first derivative is equal to zero. We don't know what its graph looks like, but we do know that its value must reach a min or max when its derivative is zero. So when the value of this function is minimum, the time it takes to arrive at work is minimum, because it is what the value of this function represent, the time it takes to arrive at work.