Optimization - Calculus (KristaKingMath)
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- Опубликовано: 23 авг 2024
- ► My Applications of Derivatives course: www.kristaking...
Understand one of the hardest and most common applications of derivatives, optimization and it's applications.
Review the open topped box example to get a better grasp on applied optimization.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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jesus christ. Thanks so much for this. I understood more in 9 minutes than in 2 hours.
She looks like my 1year College Math Lecturer. Respect and thank you for you time Miss King.
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!
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
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!
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.
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
Saving my Final score right now, thank you so much.
+Nick Koch You're welcome, I'm so glad it helped!
+CalculusExpert.com Let me know if you need a boyfriend :)
+Nick Koch Dude, "It feels good to be a gangster."
Smooth, too bad she never answered lol
Saving time and confusion, that's a win win! :) Glad I could help!
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.
Thank you so much!
You're welcome! Thanks for the comment. :)
Thank you, based math-lady.
Oh my GOODNESS! This was 2012 - 10 years ago. I THANK YOU SO MUCH FOR THIS!!!!
you're welcome, that's awesome! i'm so glad it made sense! :D
You too! Thanks for the comment. :)
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].
i would LOVE to move to New Zealand!! I've always wanted to visit! :) for now though, i hope the videos keep helping!! :D
This the new wave, get a hottie, intelligent lady to explain maths on RUclips. Profit.
dont be creepy
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.
Explanation of Calculus benefits those that truly know calculus, Thanks
I'm mesmerized by your eyes. Instant love for mathematics.
You're welcome! I'm so glad I can help! :)
This was so helpful! I lost all of my calculus notes for this chapter and you have saved my life!!!😂
Thanks for the good suggestion... I'm so glad you like the videos! :)
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 :)
This was very helpful and made a lot more sense here than in class.
So glad I could help! :)
Bummer! I wish I could have helped you earlier, but like you said, hopefully others will still benefit in some way. :)
got a test tomorrow and your video just saved me... thanks!
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! :)
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! :)
you are better than my calc teacher! Be my teacher!! :)
got a test tomorrow on this, but I understand now! thanks!
Glad you liked it!
this was complicated and messy .. you make it easy :) thank u
Glad I could help simplify it! :)
you're welcome, i'm glad it helped! and thanks for the feedback about the text of the question... that helps! :D
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! :)
I'm so glad I can help!
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!
I'm so glad they've been helpful! Afternoon classes are the toughest!
Please don't stop making videos..
I am gonna check when I will start earning
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)
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
Great video Krista; an orderly approach to optimization!
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. =)
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!
You were so good at explaining the concept and the process! You're really pretty too.
wow this was the best explanation ever
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 ;)
The world seems so easy to live in now! Thanks! :D
Thank you
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
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.
How do you go from 4x-2916/x^2 to 4x(1-729/x^3)
i was confused at this point too, but after looking closely, she had to factor out 4x to get [1 - (729/x^3)]
Good evening and thank you ma for delineating optimization to me.
Thanks!
Thanks! These surface area ones always drive me nuts, but luckily you've saved me for my calc final in 7 hours lol
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". :)
I factored out a 4x. If you multiply 4x by the factor (1-729/x^3), the result will be the previous step. :)
Awesome! Thanks for letting me know. :)
this is what I have been looking for, thank
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
Thank You Very Much!! the video helped me so much in preparation for my Electrical Engineering board exams this September 2016. :D
You're welcome, I'm glad I could help! Good luck on your exams this fall, I hope they go great!
thanks. I'll inform you if i pass the exams :D
That would be great, I'd love to hear how you do!
I don't have whats app, sorry about that!
I have a lot of worked examples on my website. :)
The explanation is clear for me. Thank you so much!
You're welcome! Glad you liked it! :)
Awesome!
You're welcome!! :)
Wooo last minute studying for calc final tomorrow
your method is very clear
Krista does a nice job. I wonder what she is doing now, 10 years after the making of this video.
Very helpful video, it helped me fill in the the minor details. Thanks!
That's so awesome! Thanks for the letting me know. :)
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? :/
Hi, in the first example, for the right endpoint, I was unsure of why you plugged in 2.
Great explanation
Thanks!
(2916/x^2) == (2916x^-2). Factoring means you subtract from what you have. Take out a 4x and you have just what she said.
You forgot a term in the expression of the surface, the surface of the box is : A = xh + xh + 2xh + 2xh + 2x^2 + 2x^2
ur amazing! passed my calc final bc of u thank uuu
I hope you're able to get back in and take it! :)
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
in the first example did you plug in f(2) because it was a critical point?
just in time for my AP Calc midterm
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 ?
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!
Will do! :)
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
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
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.
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...?
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)
Thank you so much for making this, i figured out related rates, but this just escaped me
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?
Krista you're amazing !! Thank you !
Aw thanks! Glad I could help. :)
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
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
Glad it helped. :D
Hello Krista! Why x=9 is not a 'Global' minima?
I want to say that you are a great teacher and beautiful as well!
how come you used a different right endpoint at 4:03 as opposed to the one you plugged into the derivate?
I wish you were my calc teacher, maybe i'd actually learn something haha. thanks for the help!
You are a lifesaver! thanks!
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?
you're welcome! hopefully i can be your calc teacher on youtube!! :D
Be my teacher? :D you're better than our lecturer who can't even look at the students in the eye.
This channel is spectacular! SO helpful!:)
Awww! That's awesome! Thank you!! :D
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
+Mexak A Sorry for the confusion! I'm referring to the integrals overview video which you can find here: ruclips.net/video/RjLkuYtxCrc/видео.html
+CalculusExpert.com Thank you! Appreciate that you took your time answering :)
you're welcome! :)
But what are the benefits of specialization on the nature and mathematics ground. Thank you