Dimensions that maximize the area of the rectangle (KristaKingMath)

[@XPeachezNCreamX]

This is so useful and easy to understand, you went through all the steps so nicely!!! Thank you so much!!!!

[@kristakingmath]

+Anna R You're welcome, I'm so glad it helped!

[@muhammadamanat9640]

good but speaking speed please slowwww

[@LAnonHubbard]

I did find this video helpful. It's amazing how easy it is to forget things if you don't use them for a while so this helps me keep it fresh in my brain so that I will have it in my toolbox for when I do need it.

[@cristyemru5552]

Thank you so much for clearly explaining each step! You're a life saver!

[@kristakingmath]

I took the derivative of A=50x-x^2, which was the equation for the area of the rectangle after we solved for y and plugged in. I hope that helps! :)

[@darsh4582]

Mate Ik it’s been like 8 years since this video came out but it literally saved my life today tq so much🙏🙏🙏

[@kristakingmath]

That makes me so happy, Darshen! Thank you so much for letting me know that it helped you! :D

[@lawrencedwarika8662]

You are very good at simplifying for easier understanding. I must say that to you.

[@kristakingmath]

Thanks, Lawrence! I'm so glad you think so, and I really hope the videos are helping! :)

[@johsmith2481]

Thank you so much for the help. Most of this was forgotten with time and you truly helped me relearn it all from scratch.

[@kristakingmath]

You're welcome!

[@jordanmichael801]

You're the best calculus girl on the internet. Your videos always have just what I'm looking for somehow.

[@kristakingmath]

+rusty shackleford Awesome, glad I can help!

[@jaqandlu]

thankyou very much! I able to finish my task because of this!

[@kristakingmath]

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

[@keriannee]

hey lady! u did my homework problem for me

[@kristakingmath]

Awesome! I love it when that happens!

[@biharibabu.9290]

Thank you mam for explaining in details 🙂

[@paramoregrl131]

thank you! my professor put this question on our sample test I had no idea where to start!

[@kristakingmath]

😊

[@layavardhanrockkybhai4800]

Pakodi

[@ma.pazmontano1759]

Thank you, this is very helpful!

[@kristakingmath]

Yes, normally you should check that x=25 is a maximum, but in this case, the area can't be minimized, so you know that the critical point you found must be a maximum. :)

[@CF-pb1ev]

Your videos are great. They have saved me from long frustrated nights studying

[@kristakingmath]

I'm glad they're helping!

[@calculotv1]

Excelente tú explicación. Es buena idea aplicar el Criterio de la Segunda Derivada, para verificar que en x=25 hay un máximo, Saludos.

[@ryanbrown4515]

I know this was long ago but I have a test coming up and this helped so much. Thank you!!

[@kristakingmath]

You're welcome, I'm so glad it helped! Good luck on your test, I hope it goes great!

[@ryanbrown4515]

Krista King Hey - it did! Got a 94 :)

[@kristakingmath]

Dang, that's awesome!! So happy for you, GREAT JOB! :D

[@kristakingmath]

You're welcome! :)

[@josephpliego5102]

You make everything very clear thanks

[@kristakingmath]

+Joseph Pliego You're welcome, I'm happy to help!

[@dusky4151]

I'm so confused, what did you do at 4:10?

[@adithyam3202]

Um did u figure it out? I used the formula for finding the vertex and im not sure if thats right

[@angelcross6050]

Yeah fr wtf lol, what happened?

[@ethangong6813]

Because at 4:10 you didn't explain why 50x-x square= 50-2x @@adithyam3202

[@xzaivierjames7519]

Do you happen to have the same video for the min area of the rectangle of 100?

[@SPYDER840]

@Jessy Nemati. 100/2-2x/2. Yes you can do that basic math principles

[@peppieper4786]

Great explaining thank you so much

[@inorite4553]

Well that solves that! No thanks to my Calc Professor for making something this simple so darn complicated.

[@muhammadwaqaraslam9451]

Thanks mam 😊 really nice work 😍

[@kristakingmath]

Thank you so much, Muhammad, I'm glad you liked it! :D

[@kristakingmath]

Great explanation! Thanks for replying!! :D

[@ExtremeSquared]

Rectangle area approaches zero as x or y approach zero. There's not really any math behind that, but in other optimization situations there can be multiple solutions for A'=0, one of which could be a minimum.

[@kristakingmath]

search youtube for "power rule", "product rule", and "quotient rule", and that'll start to give you an idea about how to find the derivative! :)

[@alexanderconiff8909]

Thank you so much! you have a new subscriber :)

[@kristakingmath]

Thanks Alexander! :)

[@tp7886]

How would you do this using Lagrange multipliers?

[@kristakingmath]

Ya if you're not using the information on a regular basis, it is definitely easy to forget! :)

[@sarahmontero8196]

You just saved my life.

[@kaaraayame]

Can you find the dimensions of a rectangle with semi circle of the four sides?

[@hlalelemohale7296]

Thanks a lot!

[@100equus]

Where did you get the derivative A' = 50 - 2x ?

[@kristakingmath]

In this case, the area can't be minimized. See reply by @VeryEvilPettingZoo to @SuCKeRPunCH187 lower in the comments for a great explanation about why. :)

[@JSSTyger]

Of all the possible enclosed shapes, a circle will give you optimal area for a given perimeter. It is even more efficient than a square. A perimeter of 100m will yield an area of 796m².

[@davidfinias5552]

How do you maximize the area of the circle and square?

[@JSSTyger]

@@davidfinias5552 a circle will give you the largest area for a given perimeter. Its just the nature of the shape. A square will do the same for any rectangle. A 40×40 square has the same perimeter as a 30×50 rectangle but the area is larger (1600 vs 1500). A circle with the same perimeter (160) has an area of 2037.

[@mashimaru8561]

Junior speaking,love this

[@aderoyal5833]

Couldn't you have found the second derivative to find out if the function is concave up or concave down and then conclude whether it was a maximum?

[@kundalaman]

Where are you from ? Great explanation by beautiful mam🌈

[@aishamustafa]

So Helpful! Thank you :)

[@kristakingmath]

Thanks for letting me know! :)

[@14clairebear14]

so clear thank you

[@kristakingmath]

+claire Glad it could help!

[@ThePinoyMamba]

Thank you

[@SuCKeRPunCH187]

can u have problems where they minimize the area?

[@kristakingmath]

you're welcome! :)

[@Jart988]

When you're on the last semester but gotta remember your first semester to produce a rectangular solar water heater

[@kristakingmath]

So glad you found me then! :D

[@gabrielius4603]

Why did you set the equation equal to zero?

[@ThePinoyMamba]

Is square considered a rectangle

[@carlosmertens6965]

Thank you, Ms King :)

[@kristakingmath]

You're welcome! Glad it could help. :)

[@layavardhanrockkybhai4800]

Waste fellow

[@aluisthebesttrustmeigonnag8676]

You are really teacher

[@BeyMaster20]

can u please tell me how you wud solve this without derivative

[@soulremoval]

yeah your right

[@daryllcanada2318]

Thank you ❤❤❤

[@kristakingmath]

You're welcome!

[@joseramon4301]

Why we need to find the extrema in this kind of problems?

[@kristakingmath]

Because those are the values that tell us where the minimums and maximums are. :)

[@tieramaynekanigan949]

You saved my bacon, bless this video from 2012.

[@hossamelsayed1111]

Thank you so much,

[@zahrashukri4436]

Thhhaaat was greaaat

[@kristakingmath]

Thanks, Zahra! I'm glad you liked it! :)

[@soulremoval]

idk about dividing 100-2x by 2. that seems like your breaking a rule

[@Jinsun202]

2Y = 100-2X 2Y/2 = (100-2X)/2 Y = (100-2X)/2 Y = 50-X

[@scuzz6651]

Your awesome

[@AjeetKumar-gy2hy]

your video is quiet helpful can you explain in Hindi

[@kristakingmath]

awesome!! :D

[@sarahm92]

Wow! Suscribed

[@rawrable19]

thank youuu :D

[@williamboucher9388]

Come and teach at my school you a fit maths teacher

[@DxXNA]

Hmm.. Rectangle/Square. Largest Area = (Perimeter / 4) * (Perimeter / 4). Triangle. Largest Area = (Perimeter / 6) * (Perimeter / 6) * sqrt(3). Circle. Largest Area = (Perimeter * Perimeter) / (4 * PI). But hey let's over complicate it :)

[@BioShock55Airsoft]

why did you set the derivative equal to zero

[@kristakingmath]

Because if the derivative is 0, it means the slope of the function is 0, which means the function is changing direction at that point, which means it's a critical point and either a local maximum or a local minimum.

[@BioShock55Airsoft]

Krista King ah ok thank you

[@marisolsoria6220]

I dont get this

[@bryanherrera4968]

it's

[@quiksilverblur]

you lost me at derivative. how do you find the derivative? i don't get that part. update: nevermind. i found some youtube videos explaining how to find the derivatives using the product rule and power rule.

[@Ranasmoneytalk]

I love you

[@ramboyatt3793]

isnt it always gonna be a square when you're tryna make the area as big as possible

[@SJSharks7]

muh heart

[@obayrafi2632]

Your voice is cute

[@mahzalam9405]

stop

[@shadynasty947]

Krista you smart bitch I love you

[@geotherrmal1639]

Who else did this in their head in 34 seconds?

[@ashimdas5449]

you are so beautiful

[@peteypablo55555]

I just cant learn from an attractive woman... i prefer older asian men who have minimal facial hair....no personal offense

[@gabrielcampos5495]

a Rectangle IS NOT a square

[@JSSTyger]

A square is a rectangle though.

[@layavardhanrockkybhai4800]

Not nice pakodi

[@layavardhanrockkybhai4800]

Pakodi girls