Optimization - Calculus (KristaKingMath)

[@mrzach98]

People like you are saving Calculus grades 1 video at a time. Saves me a weeks worth of confusing lectures in ten minutes. Thank You!

[@losoggyspaghetti]

jesus christ. Thanks so much for this. I understood more in 9 minutes than in 2 hours.

[@kaylawagner3295]

This was so, so helpful! Not just because of your clear explanation, but because of your calm and understanding tone. I know it sounds dumb, but I felt less pressured to rush through concepts and was actually motivated to understand each step. Thank you!

[@kristakingmath]

Awww, that makes me so happy, Kayla! Math shouldn't be scary... we should just be able to hang out and work on it at our own pace, just tackling each little piece as we get to it. I want my videos to feel peaceful like that.

[@PhilShnider]

She looks like my 1year College Math Lecturer. Respect and thank you for you time Miss King.

[@kristakingmath]

Saving time and confusion, that's a win win! :) Glad I could help!

[@DreamsConsumeReality]

You just taught me this in roughly 5 minutes skipping over what I knew. I'm SITTING in my Calc class with my foreign teacher and haven't learned crap. Thank You

[@TheJustinGreen]

Oh my GOODNESS! This was 2012 - 10 years ago. I THANK YOU SO MUCH FOR THIS!!!!

[@satnamo]

On [-2,2], the function attains its maximum value at x=2, i.e., f(2)=11 is the maximum value of the function on the closed interval [-2,2].

[@kristakingmath]

if the y-value for both endpoints is equal, then you have to call both of them local maxima. only if there is just one point that is higher than any other can you call it a global maximum. hope that helps! :)

[@nickkoch7077]

Saving my Final score right now, thank you so much.

[@kristakingmath]

+Nick Koch You're welcome, I'm so glad it helped!

[@nickkoch7077]

+CalculusExpert.com Let me know if you need a boyfriend :)

[@Mahmood367]

+Nick Koch Dude, "It feels good to be a gangster."

[@Consolous]

Smooth, too bad she never answered lol

[@kristakingmath]

you're welcome, that's awesome! i'm so glad it made sense! :D

[@dchurch2012]

Another great video! One comment on optimization problems found in textbooks: Setting up the equation to optimize is sometimes the hardest part, and the books frequently do a poor job explaining the "setup". I ran across a Revenue optimization problem that was a little confusing as to where the p(x) (i.e. the specific equation that expressed p(x)) came from; But you've done a great job of setting everything up in this demo! Thank you again.

[@kristakingmath]

Thank you so much!

[@kristakingmath]

i would LOVE to move to New Zealand!! I've always wanted to visit! :) for now though, i hope the videos keep helping!! :D

[@tichinacarmon2074]

How do you go from 4x-2916/x^2 to 4x(1-729/x^3)

[@jenniferl6212]

i was confused at this point too, but after looking closely, she had to factor out 4x to get [1 - (729/x^3)]

[@kristakingmath]

I have a lot of worked examples on my website. :)

[@kristakingmath]

because the function as it's largest value in the interval at x=2. we want to know what the value is there, so that we can say "the global maximum is 11 at x=2". :)

[@lubahristova5089]

Hi! I'm sure this is a simple answer but I'm confused at 4:19 how you went from your right endpoint being 1 to then being 2? Why is that?

[@kristakingmath]

Each of those terms is the area of one side. For example, the width is x and the height is h, so the area of one side is xh. Hope that helps! :)

[@rusticagenerica]

I'm mesmerized by your eyes. Instant love for mathematics.

[@kristakingmath]

You're welcome! I'm so glad I can help! :)

[@elisa000]

at 4:31 isn't the right endpoint y(1)?

[@ForeverPrimetime]

On 3:54 how did you get -1 on yprime(0)? Isn't it 11?

[@Smoothaltheleet]

You asked this 4 weeks ago so you might not care anymore or even remember making this comment, but she accidentally put in "6" instead of "0" for the second term (2x). So if you solved it as it looks, yes, it's 11. But if you solve it for f(0) then it would come out to be -1.

[@Ian-Threaded]

fantastic video however, not what you do to get from A'=4x-2916/x^2 to 4x(1-729/x^3) 8:02 into the video

[@Sam-js2xw]

Ian F Hi, She just factored out 4x from the parenthesis (aka Brackets in some countries). When She factored out the 4x, she had to divide 1/4x to 4x and 2916/x^2. When she divided the 1/4x to the expression, the values turned to 4x(1- 2916/4x^3). She then simplified the 2916/4 to 729 and thus she got 4x(1-729/x^3) Sorry if I used the wrong terms.

[@kristakingmath]

I only plugged them in for x. Remember that the left-hand side of the equation is y(x), so when I plugged them in it looked like y(-2). On the right-hand side, I plugged them in wherever I had an x variable. Therefore, the result for each point was something like y=-1. Hope that helps! :)

[@kristakingmath]

You too! Thanks for the comment. :)

[@HoChiMinh30abril1975]

In calculating maxima and minima for y=x³+x²-x+1 I used 1 as the right endpoint and got 2 which is the same y value as critical point -1. How do you decide which is the local and which is the global maximum in a case like that?

[@ymaramagloire2529]

This was very helpful and made a lot more sense here than in class.

[@kristakingmath]

You're welcome! Thanks for the comment. :)

[@Boomeus]

Thank you, based math-lady.

[@kristakingmath]

So glad I could help! :)

[@CharlesJacksonBey]

Explanation of Calculus benefits those that truly know calculus, Thanks

[@clefairyy]

this would've been so helpful in calc 1 last semester... oh well! i'm glad other students will be able to benefit from your videos though, you explain these concepts very well. thank you for sharing your knowledge with the youtube community :)

[@TheRatesMusic]

I found the applied example really helpful. For me it helps to see the equations "do something". Like watching a machine run helps you understand what its parts do, if that makes any sense.

[@santos131131]

(2916/x^2) == (2916x^-2). Factoring means you subtract from what you have. Take out a 4x and you have just what she said.

[@UknowthenamE16]

This was so helpful! I lost all of my calculus notes for this chapter and you have saved my life!!!😂

[@kristakingmath]

Bummer! I wish I could have helped you earlier, but like you said, hopefully others will still benefit in some way. :)

[@skeet441]

Great explanation

[@kristakingmath]

Thanks!

[@independantpeace9559]

Thank you! Oh, at 3:23 in the video Y prime of zero has a 2*6 but I believe it's 2*0. Just a friendly note. =)

[@nertin123]

you are better than my calc teacher! Be my teacher!! :) got a test tomorrow on this, but I understand now! thanks!

[@thevillage805]

got a test tomorrow and your video just saved me... thanks!

[@ivancastro365]

in the first example did you plug in f(2) because it was a critical point?

[@kristakingmath]

Thanks for the good suggestion... I'm so glad you like the videos! :)

[@kristakingmath]

I factored out a 4x. If you multiply 4x by the factor (1-729/x^3), the result will be the previous step. :)

[@jesusjesus2577]

This the new wave, get a hottie, intelligent lady to explain maths on KZbin. Profit.

[@투루-l3e]

dont be creepy

[@MsReegee]

Hi, in the first example, for the right endpoint, I was unsure of why you plugged in 2.

[@SuCKeRPunCH187]

how come you used a different right endpoint at 4:03 as opposed to the one you plugged into the derivate?

[@kristakingmath]

I'm so glad I can help!

[@Jacob-pz4ku]

my only problem is whenever the problems aren’t that simple. my teacher gave this problem Shakira is 5 miles off shore in a boat trying to escape a band of pirates! She wishes to reach a point on the coast 6 miles down shore where there is safety. She can row at 2 mph and walk at 4 mph. Where should she land the boat to reach down shore as quickly as possible I understand we are minimizing town but how tf am I supposed to know what the equation for time is when we never practice that. I’ve had an A all year and optimization is the only thing I don’t understand. My teacher makes it sound like common sense but that’s because she already knows how to solve it My teacher also said going straight down makes no sense so she didn’t solve for that but why doesn’t it if it’s twice as slow to row

[@kristakingmath]

you're welcome, i'm glad it helped! and thanks for the feedback about the text of the question... that helps! :D

[@lavenderlemons888]

i have basically this question (except there are no constraints on dimension) but the other constraint they put is that the box is 2cm cubic centimeters thick....where would i add in this 2cm into the equation? I agree with others and how setting up is usually the hardest part

[@roger72715]

Hello Krista! Why x=9 is not a 'Global' minima?

[@muskamelogbi4716]

Dear professeur may l ask you a question is optimisation a part or an exception of infinitésimal calculus ?

[@Andr295]

Very nice video. I love the instructor, too. You sound very nice and confident. One suggestion, though, it might help us visualize the problem if you present it in written form at the same time you're saying. I love your videos, though.

[@santiagocarreno5881]

Was it possible that at the end of the video the 9 was a local maximum? and if so, then what it would have mean since we are looking for the lowest value of x?

[@salarkhanmusic]

One question, at 4:02 you plugged in the critical/end points. But weren't those values for 'x' only? You plugged them for 'y' as well. Why is that? :/

[@OxLaBelleViexO]

This video really helped :) I was really confused in class when we were doing this, but now I actually get the concept of it and what to look for in the problem. But, like somebody else said, I think it would be a good idea to have text of the problem on the screen so that we can read it while your saying it, or even copy it down. Thanks for the help!

[@jamesrockford2626]

where does the 6 come from in the initial optimization equation? because there are 6 sides?

[@personc4638]

Thank you thank you THANK YOU for these videos! The thing that sucks about my calculus class is that it's near the end of the day, and I'm so exhausted by the time I get to that class, so it's almost impossible for me to pay attention (if only my school would sell iced coffee, or allow students to leave the school and come back, at least...) .I focus all of my energy in just trying to stay awake :( But these videos really save me!

[@kristakingmath]

I'm so glad they've been helpful! Afternoon classes are the toughest!

[@hanhnguyenthihong5543]

The explanation is clear for me. Thank you so much!

[@kristakingmath]

You're welcome! Glad you liked it! :)

[@vampireMido95]

this was complicated and messy .. you make it easy :) thank u

[@kristakingmath]

Glad I could help simplify it! :)

[@mariofizz13]

Thanks! These surface area ones always drive me nuts, but luckily you've saved me for my calc final in 7 hours lol

[@mohmd252]

But what are the benefits of specialization on the nature and mathematics ground. Thank you

[@adiflorense1477]

this is what I have been looking for, thank

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@PublicEnemy04]

But, in the case of the surface area, wouldn't you neglect one of the 2xh's, given that the box is topless?

[@kristakingmath]

The 2xh's are the ends of the box, so you include them. It's one of the 2x^2's that you leave out, since the box is topless. Notice from the diagram that the bottom is defined as 2x times x. :)

[@ayushgupta621]

Please don't stop making videos.. I am gonna check when I will start earning

[@neil.vezeau]

You were so good at explaining the concept and the process! You're really pretty too.

[@masteremthembu7830]

wow this was the best explanation ever

[@armando4elmundo]

Hi Krista. Just to confirm, global extrema (ie. global maxima and minima) are the same as absolute extrema(ie. absolute maxima and absolute minima)? Just different language?

[@kristakingmath]

Hi Armando, You're correct. Global extrema are also called absolute extrema. They mean the same thing. Also, local extrema are also called relative extrema. 👍

[@armando4elmundo]

Thank you for the clarification Krista!

[@kristakingmath]

Glad you liked it!

[@tashkarim2288]

On 7:47, I dont understand how you got A' = 4x(1- 729/x^3).

[@kristakingmath]

I just factored out a 4x. When you pull 4 out of 2916 you get 729. And when you pull x out of 1/x^2, you have to put an x into the denominator to compensate for the one you pulled out, so you 1/x^3. I hope that helps!

[@tashkarim2288]

Thank you very much for your help!

[@ivancastro365]

Also for the surface area of a box problem is there not another 2x^2? (2x^2+2x^2)

[@kristakingmath]

Ivan Castro No, because it's an open-top box (it has no top), so you don't include the surface area for that side.

[@ivancastro365]

integralCALC ohh thank you... rookie mistake.

[@JM995able]

Sorry but i am still in doubt from where did you get the A=xh+xh+2xh+2xh+2x^2?

[@LinkReborn]

Wait...wouldn't the area be xh + xh + 2xh + 2xh + 2x(squared) + 2x(squared)? Surface area of a rectangular prism = 2lw + 2lh + 2wh So that would make it: 2(x*2x) + 2(2xh) + 2(xh) = 4x(squared) + 4xh + 2xh ==> 4x(squared) + 6xh

[@raylance123]

Which way is the box facing

[@SergioMouraJr]

Great lectures. Can you point me to a repository of optimization questions so I can practice? Thanks!

[@ahmadtahan500]

ur explanation is simply de best ive seen till now ! but I don't really get from where u got de eqn 4x(1- 729/x3)

[@gabunir]

Thanks for posting this video! I was wondering though for the open box optimization problem... Does that mean you cannot find the maximum SA? With x=9 as the min and x=0 thrown out because it's a distance...?

[@buckeylaslo5121]

Very helpful video, it helped me fill in the the minor details. Thanks!

[@jifrazier2]

informative video, but I am curious where the 1-729/x^3 comes from (2nd step of the derivative with respect to A)

[@raulmontez2010]

Thank You Very Much!! the video helped me so much in preparation for my Electrical Engineering board exams this September 2016. :D

[@kristakingmath]

You're welcome, I'm glad I could help! Good luck on your exams this fall, I hope they go great!

[@raulmontez2010]

thanks. I'll inform you if i pass the exams :D

[@kristakingmath]

That would be great, I'd love to hear how you do!

[@kristakingmath]

I don't have whats app, sorry about that!

[@prakashchaudhary4559]

your method is very clear

[@Jesse97jwl]

Krista you're amazing !! Thank you !

[@kristakingmath]

Aw thanks! Glad I could help. :)

[@kristakingmath]

sorry about that! this was just a really broad overview video that wasn't intended to go into a lot of detail, but I have a lot more videos that are more in depth that i hope you'll check out! :D

[@Baller027]

so if it was NOT an open box. it would be 4x^2 at the end of the optimization equation correct?

[@kristakingmath]

yep! :)

[@AyodeleKayode-nb9kz]

Good evening and thank you ma for delineating optimization to me.

[@lalfalahmdjumma]

Dear , I can't understand one optimization problem written at a journal. may u plz help me. then i will send u the journal link

[@chatdiscord6047]

i am in love with your videos😍😍😍😍

[@domeee11]

At 7:46 how do you get 1-729/x^(3) ??

[@PYROxFUSION]

Awesome video! Thanks your help

[@kristakingmath]

You're welcome, Michael, I'm so glad it helped! :D

[@jamestodd6809]

This is really useful, but I'm a little lost when we go from A'=4x -2916/x^2 (which I understand as the derivate of A= 2x^2 + 2916/x) to A'= 4x (1-729/x^3) (which I don't understand how we get to this point - why is there a 1 minus involved..?) Any help would be great thanks

[@Mmssaaii]

Hi Krista! Thank you so much for these videos! I have a question; you say that "next time we are going to talk about integrals" do you refer to the remaining videos on this playlist, or another playlist? Because the remaining videos here are mostly about Optimization.. Xo

[@kristakingmath]

+Mexak A Sorry for the confusion! I'm referring to the integrals overview video which you can find here: kzbin.info/www/bejne/iJuvnKiPqd12qMU

[@Mmssaaii]

+CalculusExpert.com Thank you! Appreciate that you took your time answering :)

[@Heislegend5]

ur amazing! passed my calc final bc of u thank uuu

[@em.alharthi81]

how can i make the second derivative test !!!!!!

[@vikramwaradpande5059]

The world seems so easy to live in now! Thanks! :D

[@maraamahsan1648]

is it me or did she take the are wrong? A= 2( LB+BH+HL ) A= 2( 2x*x + x*h + h*2x) A= 2(2x^2 + xh + 2xh) A= 4x^2 + 6xh and she stated it A= 2x^2 + 6xh ?

[@kristakingmath]

This is an "open-top box", meaning that the top is missing, so you only include the bottom in the area, not the top and the bottom. That's why that extra area is missing from the formula. If the box were enclosed on all sides, you'd use the formula you have here. I hope that helps!

[@GG69355]

This channel is spectacular! SO helpful!:)

[@kristakingmath]

Awww! That's awesome! Thank you!! :D

[@kristakingmath]

I hope you're able to get back in and take it! :)

[@SeraphimKidd]

I must say that I love your videos. They're always helpful. I used to be terrible at math but ended end going from pre algebra to calc in a year! You are living proof that beauty and brains can go together! (I already believed they could go together btw. Lol)

[@kristakingmath]

Thanks Ryan! And congrats on getting control of math, I'm so impressed with your improvement in such a short period of time! Keep up the good work! :D

[@kristakingmath]

Awesome! Thanks for letting me know. :)

[@mysticalbee]

I'm in precalc. Why am I doing calc stuff? Also I try to solve it exactly like this but then I never get it right. I really don't know what I'm doing wrong.

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐