Optimization - Calculus (KristaKingMath)

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  • Опубліковано 10 гру 2024

КОМЕНТАРІ • 321

  • @kaylawagner3295
    @kaylawagner3295 6 років тому +1

    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
      @kristakingmath  6 років тому +1

      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.

  • @losoggyspaghetti
    @losoggyspaghetti 8 років тому +61

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

  • @PhilShnider
    @PhilShnider 6 років тому +1

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

  • @mrzach98
    @mrzach98 12 років тому

    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!

  • @DreamsConsumeReality
    @DreamsConsumeReality 10 років тому +1

    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

  • @nickkoch7077
    @nickkoch7077 9 років тому +27

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

    • @kristakingmath
      @kristakingmath  9 років тому

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

    • @nickkoch7077
      @nickkoch7077 9 років тому +8

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

    • @Mahmood367
      @Mahmood367 8 років тому +2

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

    • @Consolous
      @Consolous 7 років тому +1

      Smooth, too bad she never answered lol

  • @TheJustinGreen
    @TheJustinGreen 2 роки тому

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

  • @satnamo
    @satnamo 9 років тому +1

    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].

  • @dchurch2012
    @dchurch2012 10 років тому +1

    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
    @kristakingmath  12 років тому +4

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

  • @kristakingmath
    @kristakingmath  11 років тому +4

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

  • @clefairyy
    @clefairyy 12 років тому +1

    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 :)

  • @rusticagenerica
    @rusticagenerica 4 роки тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @Boomeus
    @Boomeus 10 років тому +11

    Thank you, based math-lady.

  • @kristakingmath
    @kristakingmath  12 років тому

    You too! Thanks for the comment. :)

  • @thevillage805
    @thevillage805 12 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    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! :)

  • @kristakingmath
    @kristakingmath  11 років тому +7

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

  • @nertin123
    @nertin123 12 років тому

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

  • @CharlesJacksonBey
    @CharlesJacksonBey 8 років тому +1

    Explanation of Calculus benefits those that truly know calculus, Thanks

  • @TheRatesMusic
    @TheRatesMusic 10 років тому +1

    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.

  • @ymaramagloire2529
    @ymaramagloire2529 11 років тому +1

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

  • @kristakingmath
    @kristakingmath  12 років тому

    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! :)

  • @kristakingmath
    @kristakingmath  11 років тому

    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! :)

  • @UknowthenamE16
    @UknowthenamE16 9 років тому +1

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

  • @OxLaBelleViexO
    @OxLaBelleViexO 11 років тому

    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!

  • @tichinacarmon2074
    @tichinacarmon2074 10 років тому +9

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

    • @jenniferl6212
      @jenniferl6212 10 років тому +8

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

  • @masteremthembu7830
    @masteremthembu7830 11 років тому

    wow this was the best explanation ever

  • @neil.vezeau
    @neil.vezeau 11 років тому

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

  • @mariofizz13
    @mariofizz13 11 років тому

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

  • @independantpeace9559
    @independantpeace9559 9 років тому +1

    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. =)

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @kristakingmath
    @kristakingmath  12 років тому +3

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

  • @personc4638
    @personc4638 9 років тому

    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
      @kristakingmath  9 років тому

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

  • @skeet441
    @skeet441 5 років тому +1

    Great explanation

  • @Ian-Threaded
    @Ian-Threaded 9 років тому +2

    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
      @Sam-js2xw 9 років тому +2

      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
    @kristakingmath  11 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    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

  • @vampireMido95
    @vampireMido95 11 років тому +5

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

  • @SeraphimKidd
    @SeraphimKidd 10 років тому +1

    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
      @kristakingmath  10 років тому

      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

  • @Heislegend5
    @Heislegend5 11 років тому

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

  • @adiflorense1477
    @adiflorense1477 4 роки тому

    this is what I have been looking for, thank

    • @beoptimistic5853
      @beoptimistic5853 4 роки тому

      ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐

  • @raulmontez2010
    @raulmontez2010 8 років тому +1

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

    • @kristakingmath
      @kristakingmath  8 років тому

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

    • @raulmontez2010
      @raulmontez2010 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

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

    • @kristakingmath
      @kristakingmath  7 років тому

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

  • @Andr295
    @Andr295 11 років тому

    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.

  • @SidneyGutteridge
    @SidneyGutteridge 12 років тому

    Thank you so much for making this, i figured out related rates, but this just escaped me

  • @kristakingmath
    @kristakingmath  11 років тому

    So glad I could help! :)

  • @kristakingmath
    @kristakingmath  12 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    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". :)

  • @buckeylaslo5121
    @buckeylaslo5121 12 років тому

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

  • @kristakingmath
    @kristakingmath  12 років тому

    I'm so glad I can help!

  • @LoveeTatum
    @LoveeTatum 12 років тому

    You are a lifesaver! thanks!

  • @Jesse97jwl
    @Jesse97jwl 7 років тому

    Krista you're amazing !! Thank you !

  • @elisa000
    @elisa000 10 років тому

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

  • @hanhnguyenthihong5543
    @hanhnguyenthihong5543 11 років тому

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

    • @kristakingmath
      @kristakingmath  11 років тому +1

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

  • @prakashchaudhary4559
    @prakashchaudhary4559 12 років тому

    your method is very clear

  • @chatdiscord6047
    @chatdiscord6047 2 роки тому

    i am in love with your videos😍😍😍😍

  • @AyodeleKayode-nb9kz
    @AyodeleKayode-nb9kz Рік тому

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

  • @ayushgupta621
    @ayushgupta621 7 років тому

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

  • @ForeverPrimetime
    @ForeverPrimetime 8 років тому

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

    • @Smoothaltheleet
      @Smoothaltheleet 8 років тому

      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.

  • @polvin2487
    @polvin2487 12 років тому

    I want to say that you are a great teacher and beautiful as well!

  • @santos131131
    @santos131131 11 років тому +1

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

  • @kristakingmath
    @kristakingmath  11 років тому

    Glad you liked it!

  • @govou3000
    @govou3000 12 років тому

    You are right bro!!!!!!!!! she is amazing man!!!

  • @GG69355
    @GG69355 11 років тому

    This channel is spectacular! SO helpful!:)

  • @vikramwaradpande5059
    @vikramwaradpande5059 10 років тому

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

  • @lubahristova5089
    @lubahristova5089 6 років тому

    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
    @kristakingmath  12 років тому

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

  • @azawee90
    @azawee90 11 років тому

    ur just gorgeous !! plus u helped me a lot to be prepared for my test tomorrow.. Big thanx

  • @KarasuHebun
    @KarasuHebun 11 років тому

    Wooo last minute studying for calc final tomorrow

  • @jesusjesus2577
    @jesusjesus2577 5 років тому +12

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

  • @kristakingmath
    @kristakingmath  11 років тому

    Awesome! Thanks for letting me know. :)

  • @Moh20ish
    @Moh20ish 12 років тому

    That was really interesting Krista :)

  • @PYROxFUSION
    @PYROxFUSION 5 років тому

    Awesome video! Thanks your help

    • @kristakingmath
      @kristakingmath  5 років тому

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

  • @Darhyun
    @Darhyun 11 років тому

    Thank you so much! You really helped me a lot.

  • @connor8094
    @connor8094 12 років тому

    I wish you were my calc teacher, maybe i'd actually learn something haha. thanks for the help!

  • @nikhiMD
    @nikhiMD 9 років тому

    I think 22 people mistook the unlike button for the like button.
    You're amazing, so keep doing what you're doing~
    Btw, do you have heterochromia? Cause your eyes look amazing!
    Love, a sophomore in high school ;)

  • @Jacob-pz4ku
    @Jacob-pz4ku 5 років тому +1

    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

  • @brogrammer6
    @brogrammer6 11 років тому

    Thanks to you I passed my calc class!!!!!!!! Just wanted to come back and say you're amazing, and damn cute. Thanks for everything girl

  • @kristakingmath
    @kristakingmath  12 років тому

    Awesome!

  • @fezamto940
    @fezamto940 5 років тому +3

    Thank you, you’re my favorite ✅✅✅✅✅

  • @lavenderlemons888
    @lavenderlemons888 10 років тому

    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

  • @ivancastro365
    @ivancastro365 9 років тому

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

  • @kristakingmath
    @kristakingmath  11 років тому

    That's so awesome! Thanks for the letting me know. :)

  • @tashkarim2288
    @tashkarim2288 8 років тому

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

    • @kristakingmath
      @kristakingmath  8 років тому

      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
      @tashkarim2288 8 років тому

      Thank you very much for your help!

  • @lostchild
    @lostchild 11 років тому

    cool , you guys just saved my life

  • @kristakingmath
    @kristakingmath  12 років тому

    You're welcome!! :)

  • @kristakingmath
    @kristakingmath  12 років тому

    Thanks!

  • @PublicEnemy04
    @PublicEnemy04 10 років тому

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

    • @kristakingmath
      @kristakingmath  10 років тому

      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. :)

  • @kristakingmath
    @kristakingmath  12 років тому

    Glad it helped. :D

  • @maraamahsan1648
    @maraamahsan1648 7 років тому +3

    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
      @kristakingmath  7 років тому +7

      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!

  • @elenagaridis9392
    @elenagaridis9392 11 років тому

    Thank you for this great video!!

    • @kristakingmath
      @kristakingmath  11 років тому

      you're welcome, i'm glad you liked it!! :D

  • @RogerKlauser
    @RogerKlauser 10 років тому

    Final on Thursday. Thanks for helping. :)

    • @kristakingmath
      @kristakingmath  10 років тому

      You're welcome! Good luck on the final!!

  • @ivancastro365
    @ivancastro365 9 років тому

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

    • @kristakingmath
      @kristakingmath  9 років тому

      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
      @ivancastro365 9 років тому

      integralCALC ohh thank you... rookie mistake.

  • @Baller027
    @Baller027 10 років тому

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

  • @HoChiMinh30abril1975
    @HoChiMinh30abril1975 11 років тому

    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?

  • @kristakingmath
    @kristakingmath  11 років тому

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

  • @santiagocarreno5881
    @santiagocarreno5881 8 років тому

    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?

  • @MsReegee
    @MsReegee 11 років тому

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