Optimization Calculus 1 - 2 Problems
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- Опубликовано: 29 сен 2024
- Calculus Optimization Problems: 3 Simple Steps to Solve All
Step 1: Get Two Equations
Step 2: Plug One Equation into the Other & Simplify
Step 3: Take the Derivative of this New Equation and Set Equal to Zero & Solve
That's it - Done - Happy Day! ;-)
This video contains a lesson and 2 step by step examples.
Example 1: Optimization Overview (product and sum of 2 numbers)
Example 2: Optimize the area of a pen for a dairy farmer
More Optimization Examples at Calcworkshop.com
1 - Optimize the area of a geometric shape (rectangle)
2 - Optimize the volume of a geometric shape (box)
3 - Optimize the area of a corral for a rancher
4 - Optimize the shortest distance between two points and a curve
5 - Optimize the area of text on a page
For more lessons and step-by-step examples on all topics in Calculus
Calcworkshop.com
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my left ear enjoyed this :). also great video thank you!
+The Circle got scared thouught my right earbud broke haha
3 months into calc and I want to jump into the ri era and float away. None the less, great video.
Love your video! You are very clear and easy to understand. I will go to your videos for help in the future. Thank You!
Thanks Jessica!
Excellent instruction. Thank you.
Hey Bill Holt - thanks for the compliment!. :)
Awesome explanation! I wish my teacher is more like you~
Do you know how to use a matlab code to solve complex optimization problems?
Excellent explanation. Made a seemingly impossible concept extremely understandable.
+Aziz Elbasheir :)
Woah! This is crazy!
I watched the video up 2:19 and now I can solve any optimization problem.
Thank you so much.
Love it...
no kidding!
None of her markers have caps
lol
😂😂
am i the only one who gets anxiety from her not closing her markers???
Thanks for the crystal clear explanation of Optimization.
Hi Musa M.F. Kouma-Deito Kromah - You're very welcome. I'm glad it helped you out.
Omgg this was amazing! You explain the concept so clearly. I can actually do optimization now.
You explained so well my kid brother will even understand what you're doing.
The derivative is equal to zero at relative minimums and relative maximums. Knowing this, is it safe to conclude that the answers you obtain in the first problem are both minimums? Is it possible that one could be a maximum?
The first example is better understood if you use example Area = x*y = 198. Find minimum perimeter of a rectangle 2(x+y) which has Area(x*y) = 198 . Also do you know where I can find a Simplex program for multivariable linear optimization. Thanks.
Very Helpful Thank you! Keep up the great work, this is much appreciated.
thank you so much!
The Dora of Calc teachers and I mean that in a good way great explanation!
thank you sooooooo much you saved my life
I learned so much, thank you i really appreciate it !!!!!!
Great video, my left lobe can optimize anything now!
This was so amazing! So clear and easy to understand! THANK YOU
Why couldn't you have been my calc teacher. it makes way more sense.
I thought these were all bots ngl. But it’s true she basically explains how you should go about optimization. It’s really hard for professors to even explain it so they just go on along chugging numbers. Thanks woman 🙏🏾
00:30 "...optimize my checking account..." 🤣🤣 finally! I'm watching the right YT video!
THANKYOUUU VERY MUCH! THIS HELPED ME A LOT FOR OUR CALCULUS TEACHER AINT DOING HIS JOB AND IM TOO LAZY TO READ MY BOOK. ILYSM.
Thanks for the explanation, I really loved how much you made it simple!!
I enjoyed it
Thanks a lot for clear explanation. Any more videos on calculus & linear algebra coming? See forward to it!
you rock!!
thank you
Thank you for you fantastic explanation. I love your energy. I will definitely consult your website.
Why can't product be the product of three numbers? Is optimization only for 2 variables?
im 10 years old and i can understand calculus EASILY
lifesaver!!!
Thank you so much it help me a lot💓, rooting for your more videos 💪
Thank you so much! I finally understand optimization so much better now thanks to you :D
Those 21 dislikes are probably from some triggered mathmaticians
Ahmed Al-Ahmad well
I'm gonna show my grandkids this video when they're struggling with optimization.
Thank you for your explanation of optimization problems. I watched this after going over this in my last lesson and it really help solidify the subject matter. I didn't really notice I was plugging into two equations every time and now that i know what to look for, I feel confident. Thank you again!
Woah!!! you are amazing. You just made it simple for me. Thank you
Hi, I am looking for a formula to calculate the lenght of a rope enrolled flat on a deck. Kind of spiral enrollment every boat lover have seen.
Simple and clear!!!Great job!Thank you for your video!!!
so I have watched about every video on optimization and I couldn't do it at all until I watched this video. Thank you. Don't ever stop teaching math.
Thank you so much for your kind words. :-)
thank you so much. I don't think it is possible for anyone to simplify it more than you have.
Dear professeur, is optimisation calculus a part or an exception of infinitésimal calculus ?
I love this tutorial, super fluent and easy to understand!!!! amazing, helped so much:)
Thank you so much. It really helped.
Calculus in plain English! Thanks for putting the EXACT steps needed to solve optimization problems!
you're welcome!
WOW I wish my college professor could explain calculus like you ... would make my life much easier!!!!
Thanks for the video.
Glad you enjoyed the video!
Nice explanation...
Thank you
used your method to find max area of a rectangle bound by a certain function. helped me out a lot. thanks!
+Brad Ingram - Rock ON!
Thank you! This was so much help
where did u go!? I wanna look at a rancher too!
Area is length times breath
this is so helpful thanks so much!
But how do you determine if it's a maximum or minimum
Great video.
John Brasely :-)
HI.. Its just so awsum,,
You are going very good Mam :) (Y)
Maxima and Minima
the first derivative test
optimization
Techniques of integration (power of sin and cosine, Trignometric substitutions, integration by parts, Rational functions, etc)
Differentital equations
Coshy Problems
Hi Anam Amin - Thank You SO much!
Mam..!! Thank you so much. :) I need some more examples..If you can provide me some good notes for maxima/minima better understanding?
good video... when i watched it, i only got left audio out of the video--dunno if this is a problem on my end or just the video
Hi Nikolaus Smith-Simmons - not your end, the video was initially encoded in mono. :-)
hello, i have to find max or min for a function of 3thd grade, the problem is that when i do the f'(x)=0 i get x1= 5/11 and for the other two :x2= (-2+5x i )/16,,x3=(-2-5x i )/16. -->> because D
resilda hajdini Hi. What this means is that you have only one critical value (potential max/min) because the other two values are imaginary. To determine what type of extrema you will test your critical number on a number line, or you will find the second derivative and set it equal to zero. What you should see is that the two imaginary values you got from the first derivative test will affect/verify the change in concavity.
thnxxxxxxx you a lot !!!!! really thnxxxx
A great calculus teacher!
My left ear enjoyed this video
Best videos to help you with calculus all over youtube
Thank you so much Syed!
how are we able to determine the domain?
veryy kool
nice explanation
nobody said it was this easy!!! wow
You are an excellent teacher. Thank you so much for these free videos.
Hi Cooked Vegan Fitness - Thanks! I'm so glad they helped. :)
You are awesome!!
I have to take a test in 2 hours, and you just explained it so clearly. Thank you so much. *Please wish me luck
Thank you so much for this video! It really helped me understand optimization once you broke it down into three steps and made it ALOT less daunting!
great video!
thanks to you i passed my finals :)
That's great news!! Congratulations!
First teacher I have seen that seems to understand the main problem comes from setting up the two equations. Good stuff, I have a test over this in the morning and your explanation helped a bunch! 🤞
I appreciate your quick joke at 12:10 on minimum ink in the green dry-erase marker: "Oh my goodness, it's a minimum!" Right to the situation! :-)
haha - glad you enjoy my quirks.... :)
Well explained.
Thank you so much! finally helped me understand the difference between solving one for the max and one for the min
Like how would the question be different if it said the sum is a maximum??
For a max perimeter you would let b go approach infinity and h approach zero.
You could always add more fence when working with 2d in reality the fence has a thickness so any fence post can only come so close to another. Also there needs to be enough room for the cows. So you could say that b> say 5 feet. And h>5 feet. This would have a max perimeter at h=5 and b= 36000. This has a perimeter of 72005 square feet.
OMG i love ur vids
thank you very much
This was really helpful, she explained this concept very well (I only wish I had watched this before my exam lol)!
you're amazing
Why is it 192 ^-2 ?
First time commenting on a tutorial video.. This was just perfect! Thank you soo much
Subscribed :')
Hi Salma Almekhlafi - wow, Thank You for the compliments! :)
Salma Almekhlafi :-)
Calcworkshop.com - Calculus Videos You're most welcome
can you do a series on derivatives, implicit differentiation and using log as well e^X in derivatives
In your first problem you solved, how do we know that the sum of the two variables will be a minimum not a maximum?
Sorry if a reply to this doesn't matter anymore but: I think you just approach continuing from those answers as if you were trying to find intervals where the function increases and decreases. (Yknow like if you're working on a problem for curve sketching.)
You could take the second derivative at that point. If it is positive then it's a min. If negative it's a max.
you have summarized it nicely, pretty easy to be digested, keep on good work. it helped a lot.
thanks you so much
Shes awesome i wish all her videos were on youtube. 😞😞
Hey +Andrea Santiago - Thank You for your kind words. :)
Unbelievable !! I wish I'd had teachers like this in college who are so clear and logical, she's like a walking syllogism !! thanks!
Dude I thougt my other earbud got broke, nice video btw!
Really wish my teacher explained this as clearly as you do
There’s tons of good videos on this but yours made the most sense to me
You're welcome Nelson!
great exercise.
Thanks for making this into a short video! :)
Well done.
Thank youuuuuyuu!!!! Right to the point! Simple! And with real life examples! Love you!
Hi +ElKePoN Adventures - Thanks for the kind words. :)
Awesom🙂
The most amazing video on youtube
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