Finding Local Maxima and Minima by Differentiation

What else is differentiation good for? Well if we are looking at the graph of a function, differentiation makes it super easy to find where any local maxima and minima occur. This act in itself has many applications, but before we learn those, let's just learn how to find the maxima and minima!
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Thank you, professor Jesus.

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even after he started with “it’s professor Dave...” 🤧

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He looks like so!

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You know what they say, "God is always there for you even when your math teacher sucks"

[@leo0918]

Sir 'Professor Dave Explains', i just wanna let you know how grateful and lucky i am. watching your calculus video is enlightening. i am from philippines, currently out of school. i am doing some review on my math subjects before re-enrolling again. i am also a self learner, and thanks to you because i am on a great progress with calculus (self taught). i never learned it from the school, i learned it on your calculus videos and some old books. you saved me. im hoping that someday, if i happen to meet you in person, i have already achieved my dream of becoming a good mathematics teacher. Thank you so much sir.

[@ProfessorDaveExplains]

good luck!

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it is very good exblain

[@kumaransrinivasan2639]

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From Philippines too❤️

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[@RedEyedJedi]

He says "that one was pretty simple" just as my brain was about to explode.

[@drumpfbad5258]

Are you in AP calc?

[@mariakhan6090]

It's very simple for us Asians 🤷

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​@@mariakhan6090 I'm part Asian too but I'm mainly English. If I pointed out I find programming easy, purely because I am English, people would think that was racist.

[@photocide17]

It was literally the easiest.

[@froopi2]

Noob

[@annyan904]

this man is indeed a true knowledgeable person.....knows how to apply his learnings practically......his videos should have more views but unfortunately people dont care to learn things in such detail.....but people like me are a fan of his videos.....lots of love and respect professor dave..... moreover people don't realise a crucial thing if learning can be put practically there will be no need of tedious practicing......maths would become fun....thanks dave....i am not financially that strong to support your channel....but someday i will...thanks please continue making such videos on valuable topics

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U like ellipses perchance?

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Your great at what you do man! The reason these specialized videos don’t get many views is because only a select few need this type of information and your competing with khan academy etc. As more time goes on these type of specialized videos will have so many views and help so many people. I’ve already seen you covering more broad topics and they have a ton of views and are structured excellently for learning. I come to your videos for all my topics your amazing!!

[@ProfessorDaveExplains]

woohoo thanks! yes i think that once i am finished with calculus i will find a way to advertise a little bit and then it will get a more appropriate viewership. but thanks for watching and spread the word!

[@robertbocklage1249]

@@ogstephh shut up idiot

[@pawanwadhwa4063]

Thanks I was struggling with this ..from quite a long time and finally got it. Thanks once again.

[@aisharona7421]

You just make my work easy .. Thank you so much from South Africa ❤

[@MrMarkgyuro]

thank you Professor Dave! I learn math on my own and your videos make my life easier and more fun.

[@sebastianmorales4183]

Thank you Mr. Professor Dave, I would like to thank you for explaining this concept. Now I understand local maximum and minimum. May God Bless You and His Peace Be Upon Upon Always!

[@parmeetkaur6117]

You had explained the whole concept in clear and precise way.... Very fantastic teacher u are

[@jojappakoyyuru8301]

a great source of required information.....Thank you sir...

[@asdffdsaemantsal9175]

thanks man, 2020 put me in online and instead of reading the notes they give us imma just look up videos on how, thank you

[@shreyaa9180]

Thank you so much sir.. this was too useful and helped me a lot..

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Professor Dave is the best.

[@Sam-qf3sc]

Thanks for such a great explanation

[@GoldenSpike300]

Professor Dave is daddy. Literally has gotten me through physics and calc this year.

[@alexdefoc6919]

Sir. I wanna you that you really helped me understand implicit and relative differenciation

[@rexelcier8768]

professor dave thnx for making this video i have my math exam in 3 days and this helped me a lot in learning maxima and minima thank you sir

[@RaviKant-uk5ok]

Keep on enlightening inchoate mathematics tyros. Thanks a lot.

[@shashilata4506]

Fantastic explanation sir

[@Carlynimrshuff]

this one helps me a lot like im really stuck right now at my calculus. and im very afraid that my top grade goes down. this one really helps sir especially that we are now in new normal class❤❤

[@johnkennethmarta691]

Thank you, Sir Dave!!!

[@chxxbikim662]

Thanks for your great explanation.,.👍

[@MairajKhawar]

Sir excellent method of teaching

[@santothomas8300]

how to find the maxima and minima of a damping signal as it has more than 1 point with m=0?

[@11a-vvmsrirangasuthan.t62]

At last I finally got a video which taught me the concept rather than problems

[@mr.unknown1070]

Professor Dave is like 'Marshmallow of educational field'. He is perfect at every subject 🤯🤯🔥🔥🔥🔥🔥

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I’m not even in calc yet. I’ve exclusively watched these and can say I have a firm understanding of everything he says. Same for organic chem. Someone get him an award

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The holiest video in all of KZbin

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A sent from heaven!! Thank you!!

[@chupacabra304]

My teacher needs to learn from this guy how to explain

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Great review!

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Very clear, very nice

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Nicely explained

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Your intro was awesome!!😅😂😂😂

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If there is one job in the world that can be this helpful and important in the world besides medicine it's teaching

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Coming up to my second semester exams and this helps so much. What you do In 6 min takes my teacher 3 lessons

[@crish8400]

thank you so much, i was about to cry because i didnt know what to do =)

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About to give up maths but thankyou professor ❤️🥺

[@shuvotechadda4162]

Thank u *Professor* --😍😍

[@ethanhunt8274]

Explain by profferser Dave is excellent

[@udechidiogo715]

Thank you, this was really helpful 😁

[@pandeephny]

Hi Prof, @3.07 by looking the graph i can say local min & max are -2,+2 but the solution you have is 0,2. Im bit confused

[@aymansaif1958]

Thanks bro 👍

[@elijahmusanda5731]

Why did I feel like a baby in the first place??

[@aashsyed1277]

Also make a video about differential equation

[@reyhanashik2123]

thank you so much

[@LMAO-fs1bt]

Thank you sir

[@vedang371]

Professor Jesus helped me pass my class, Thankyou

[@SonMulti]

For the 'comprehension' problem, why did you inset plus 2 and minus 2 into the equation afterwards?

[@ProfessorDaveExplains]

because that's where the local maximum and minimum occur, and we want to get the exact maximum and minimum values

[@user-sv2qj2nd1t]

in the first example is y1 =1 and y2 =-3 ?

[@aashsyed1277]

You have not made a video about integration by parial fraction decomposition

[@memenchance1747]

Thanks bro 👍👍💯🔥🔥🧠

[@ntambi2624]

Thanks prof

[@dpkd3198]

Really it helped 😇

[@m3dz560]

thanks a lot!!!!

[@itsinfinity2378]

Can you tell me in which grade it is studied

[@recoilzriot6211]

3:10 If the curve is inverted W.R.T x-axis. Then also you will get 2 extrema at x=0 and x=2 But how to tell if that's maxima or minima

[@kishorekannan652]

Subs value in f(x).. smaller value is minima and maximum value is maxima

[@ddnnd7741]

Ur a blessed soul 🙏

[@NAYANIKASAHA-st7uv]

Is x^3 will never have maxima or minima, incase interval given then also no maxima or minima ? Plz someone help

[@streamxstudio186]

I can just say love u sir..........

[@MyMinecrafter97]

I've passed my calculus classes already, but it's fun to watch it again

[@prakhargupta2960]

But how do we know which root at 3:14 was max or min without a graph?

[@srianshuray2861]

check if after differentiation if value more than 0 then minima if value less yhan zero is maxima

[@sanchi7410]

Thankyou

[@mrw5258]

Lmaooo I remember learning that topic from this video and now I'm revising it . Nice vid

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hello sir,I want to receive lectures of calculus from you. how can I get that? sir.

[@kolanpakakalyan5929]

Thanks 👍

[@pranjalverma3501]

very nice video

[@Theanymemetor]

I have a question. I know this is a bit late but why did we plug back in 2 and -2 in the f(x) function? Is it because to find the (x,y) values? Please let me know and thank you!

[@rxsvie]

yup to locate the maximum and minimum points :D

[@Theanymemetor]

:3@@rxsvie

[@cherryhenderson4920]

I don’t understand for the checking comprehension question. How did you get x=-2? I get how you got 2 but not sure how -2 came about?

[@ProfessorDaveExplains]

(-2)^2 is also 4

[@roshinsleebac4709]

Can u plz give a simple daily life application of maxima and minina! From many videos i noticed that it helps in economics to maximize and ,in efficienting packing etc..But none of them explains how it is done...well,after finding local maximum,how can it help to maximize profit?!!plz help to figure it out

[@9308323]

That's not a "simple daily life application." There's a reason why people study these things for years. However, to answer your question: for this, you'd have to have your revenue and cost function. Subtract the C from R, and from there, just find the local maximum and it should tell you how much you need to set the price for the product. If you want to take it a step further, you can minimize the average cost.

[@carultch]

Here's a simple example of optimization, that you could easily understand its application to real life. Suppose we need to transport cargo from an island to a warehouse. Consider a straight shoreline that runs east-west, and the warehouse is L=100 km east of the island, also on the shore. Assume the road runs directly along the shore and any inland travel distance to get to the road is negligible. The island is d=50 km south of the shore. We need to determine where along the shoreline to build our dock for unloading the ship, that will minimize the amount of fuel consumed. Suppose a truck takes 1 liter of fuel to drive 1 km (a rate we can call T) and suppose a ship takes 5 liters of fuel to transport the same cargo a distance of 1 km (a rate we'll call S). Define the origin at the point on the shore directly across the water from the island, and define distance x as the position along this shore where the dock could be located. Assume only a 1-way trip for simplicity. A: find an expression for the fuel consumed by the truck, as a function of dock location x B: find an expression for the fuel consumed by the ship, as a function of dock location x C: find a function f(x) for the total fuel consumed, by combining expressions from parts A and B. Answer: f(x) = T*(L-x) + S*sqrt(x^2 + d^2) D: Take the derivative of this function. E: Set this derivative equal to zero, and solve for the optimal value of x that minimizes fuel consumption. Answer: x=(d*T)/sqrt(S^2 - T^2), which happens at x=10.2 km.

[@Elitea20]

Are you an actual professor you know everything

[@carultch]

He answers this in one of his "Ask Professor Dave" videos.

[@ros2186]

U r good

[@Fore-bp8jp]

I got a little confused at the solution at the end, which of the solutions were maxima and minima'

[@harrymed6799]

Thanks from India

[@tGoldenPhoenix]

Calculus is magic, derivative is fucking wonderfulll!!!!

[@tGoldenPhoenix]

Done this lesson.

[@linakruger1280]

Any link where I can find a whole. Playlist on applications of differentiation and integration?

[@ProfessorDaveExplains]

Check my calculus playlist!

[@everythingiseconomics9742]

This is the entire economics profession

[@damandeepsingh8542]

Very good

[@ParthTyagi-kq6th]

If there are more then 1 local maxima/minima can we find all of them

[@codexcodexcodex]

But, how about how high the local maxima and minima? Is it important?

[@maheshiwijesinghe7639]

Helpful 😇

[@a.m.a.b147]

Dave I feel like f prime of X isn't right on 3.46

[@jessicasosa6480]

How did you end up with 1,-1? I’m lost there.

[@GG-dm2qm]

I had a math question, how can I send it to you?

[@arslanyaqoob9534]

You did put the x values once in first derivative and then in the last problem you did put the value in the original function? Why

[@robloxeatskids8907]

You find the x values for which the slope is 0 using the derivative and plug those x values into the original function to get the y value.

[@ahmad_hun]

I just really love intro

[@aneelaamin2235]

very good,

[@ArnavGarg-rl6qh]

Bro is the 💎. And is found in the caves of KZbin i am so lucky to find him

[@rahullunthi6313]

Professor Dave question(-tsquared+4t+4)

[@isaacfandakly]

That doesn’t factor

[@amnfox]

How do you find the maximum number of zero crossings?

[@pranjalarora3193]

Degree of equation= maximum number of zero crossing

[@darkshadowsvideo]

professor dave im so sorry i strayed from your teachings i didnt know you had calc lessons

[@ProfessorDaveExplains]

Yep 35 part playlist, check it out!

[@samjoy3247]

can someone explain to me why at 3:50 2x^2 disappears?

[@tirkdiamond]

Kind of late but in case anyone else is wondering about that : x^2+1 -x *2x = x^2+1 -2x^2 = x^2-2x^2+1 = -x^2+1

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bruh i love you so much ur better than khan academy and ur way cooler too cuz u debunk clowns like flat earthers

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perfecto

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thank u mr xaxo

[@guptaji7733]

The intro ❤❤

[@009harshaveena.k2]

What if the critical point zero

[@_CertifiedHoodClassic]

Lmao i just stared at the video thumbnail for a bit, then i understood exactly what to do 😂😂😂. im just commenting to make sure you know u helped. 👍

[@srilekhapachari9625]

Tq sir