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. :)
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.
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. :)
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.
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 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.
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.
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.
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 :)
This is so useful and easy to understand, you went through all the steps so nicely!!! Thank you so much!!!!
+Anna R You're welcome, I'm so glad it helped!
good but speaking speed please slowwww
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! :)
I'm so confused, what did you do at 4:10?
Um did u figure it out? I used the formula for finding the vertex and im not sure if thats right
Yeah fr wtf lol, what happened?
Because at 4:10 you didn't explain why 50x-x square= 50-2x @@adithyam3202
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. :)
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.
Where did you get the derivative A' = 50 - 2x ?
Do you happen to have the same video for the min area of the rectangle of 100?
Can you find the dimensions of a rectangle with semi circle of the four sides?
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. :)
Thank you so much for clearly explaining each step! You're a life saver!
Mate Ik it’s been like 8 years since this video came out but it literally saved my life today tq so much🙏🙏🙏
That makes me so happy, Darshen! Thank you so much for letting me know that it helped you! :D
How would you do this using Lagrange multipliers?
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.
hey lady! u did my homework problem for me
Awesome! I love it when that happens!
can u have problems where they minimize the area?
You're welcome!
can u please tell me how you wud solve this without derivative
Thank you so much for the help. Most of this was forgotten with time and you truly helped me relearn it all from scratch.
You're the best calculus girl on the internet. Your videos always have just what I'm looking for somehow.
+rusty shackleford Awesome, glad I can help!
Is square considered a rectangle
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! :)
Excelente tú explicación.
Es buena idea aplicar el Criterio de la Segunda Derivada, para verificar que en x=25 hay un máximo, Saludos.
You're welcome! :)
thank you! my professor put this question on our sample test I had no idea where to start!
😊
Pakodi
Well that solves that! No thanks to my Calc Professor for making something this simple so darn complicated.
I know this was long ago but I have a test coming up and this helped so much. Thank you!!
You're welcome, I'm so glad it helped! Good luck on your test, I hope it goes great!
Krista King Hey - it did! Got a 94 :)
Dang, that's awesome!! So happy for you, GREAT JOB! :D
Why did you set the equation equal to zero?
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?
You are very good at simplifying for easier understanding. I must say that to you.
Thanks, Lawrence! I'm so glad you think so, and I really hope the videos are helping! :)
Your videos are great. They have saved me from long frustrated nights studying
I'm glad they're helping!
Thank you mam for explaining in details 🙂
Great explanation! Thanks for replying!! :D
thankyou very much! I able to finish my task because of this!
You're welcome, I'm so glad it helped, Jaque! :D
@Jessy Nemati. 100/2-2x/2. Yes you can do that basic math principles
When you're on the last semester but gotta remember your first semester to produce a rectangular solar water heater
Why we need to find the extrema in this kind of problems?
Because those are the values that tell us where the minimums and maximums are. :)
Thank you, this is very helpful!
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.
How do you maximize the area of the circle and square?
@@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.
Ya if you're not using the information on a regular basis, it is definitely easy to forget! :)
Thanks mam 😊 really nice work 😍
Thank you so much, Muhammad, I'm glad you liked it! :D
Thank you so much! you have a new subscriber :)
Thanks Alexander! :)
Where are you from ? Great explanation by beautiful mam🌈
You make everything very clear thanks
+Joseph Pliego You're welcome, I'm happy to help!
Great explaining thank you so much
So glad you found me then! :D
Junior speaking,love this
you're welcome! :)
You just saved my life.
idk about dividing 100-2x by 2. that seems like your breaking a rule
2Y = 100-2X
2Y/2 = (100-2X)/2
Y = (100-2X)/2
Y = 50-X
why did you set the derivative equal to zero
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.
Krista King ah ok thank you
You saved my bacon, bless this video from 2012.
So Helpful! Thank you :)
Thanks for letting me know! :)
so clear thank you
+claire Glad it could help!
Thanks a lot!
Thank you ❤❤❤
You're welcome!
I dont get this
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.
Thank you
isnt it always gonna be a square when you're tryna make the area as big as possible
yeah your right
Thank you, Ms King :)
You're welcome! Glad it could help. :)
Waste fellow
You are really teacher
awesome!! :D
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 :)
Thank you so much,
Your awesome
your video is quiet helpful
can you explain in Hindi
Thhhaaat was greaaat
Thanks, Zahra! I'm glad you liked it! :)
Come and teach at my school you a fit maths teacher
it's
thank youuu :D
Wow! Suscribed
Who else did this in their head in 34 seconds?
I love you
Your voice is cute
stop
muh heart
Krista you smart bitch I love you
I just cant learn from an attractive woman... i prefer older asian men who have minimal facial hair....no personal offense
you are so beautiful
a Rectangle IS NOT a square
A square is a rectangle though.
Not nice pakodi
Pakodi girls