Thank you!!!! You just saved me so much! I was in a time crunch, and your video was concise, easy to understand, and visually appealing. You have my neverending gratitude.
Thank you soooo much! This is the most helpful video I have ever watched in my entire life. I hope everything in your life goes right for you. Thank you!!!!!
The equation you find for A' is the equation that models how fast the surface area of the cylinder is changing as the radius changes. For example, if you want to know how fast the surface area is changing when the radius is equal to pi, you would plug pi in for r into the equation for A'. If the value you get back is positive, then this is how fast surface area is increasing at r=pi. If the value you get back is negative, then this is how fast surface area is decreasing at r=pi. :)
I know this is a late comment, but I had this type of question come up on my math homework and I don't remember the teacher explained this during class. I found your video and it was so helpful! Thank you so much!
Thank you so much, also random but until watching this video I didn’t realize how nice it is to see a woman explain math. Idk it made me feel really happy!
For those just rote learning that they should differentiate - here is little intuition: since the relationship between radius and area is parabola, dA/dr = 0 is either maximum or minimum. But the graph has no maximum - you can increase the radius up to infinity and the area will just keep on increasing. So this means when dA/dr is 0, we have the lowest point of the graph and that is the radius with lowest area. Simple yet genious application of calculus.
Great explanation!! It only occurred to me recently that there ought to be a formula for minimizing the surface area of a cylinder, both to reduce construction costs, but also to limit radiation heat loss or gain. Moreover, the height to radius should be ratios, scalable to any size. I love geometry and trig, but never a big fan of calculus. Thanks for a fairly intuitive explanation. I was planning on using a spreadsheet for trial by error or range.
i divided both sides by 4. since that gives me 0/4 on the left side, i just have 0. i get 4/4 on the right side, which just leaves me with 1. the r^2 disappears when you take the cube root of both sides. :)
This morning I was trying to remember how to work this problem out (I am in my sixties) and came across your video. Thank you. So:- Expanded out: r= (approx) 5.41926, h=(approx) 10.8385, d=2*r = (approx)10.8395. So maximum volumn for min surface occurs when height = the diameter.
Muchas Gracias, todo se puede lograr. Amo la Ciencia y la Tecnologia, Siento que todo se puede lograr con tus Clases. Gracias Maestra por su tiempo. ES POSIBLE. Matemáticas un gran misterio.
Thank you for this! Was just talking about this concept with my son (high school). He's excited about taking calculus soon. You're an excellent instructor 🙂👍
it's a basic principle of differentiation, you multiply the coefficient/constant by the exponent and subtract 1 from the exponent, and -1×2000=-2000 r^-1-1= -2
hi i have a question im confused at 7:09 how you went from 2000 to 500 cause im trying to substitute my question into your working if you get what i mean so right now im at (0= 4 pi r3- 750/ r2 ) sorry if this doesn't make sense
Would also be interesting to show in the conclusion to the video that area is minimized when h=2r (when the height of the cylinder equals its diameter). Just an interesting observation.
what does the can look like with the minimized surface area with its original volume. How is it gonna be different from the original shape of the unoptimized can?
integralCALC lol Thank you Krista What a beautiful name! You are the smartest and nicest You helped me pass my exam yesterday I'st that awesome Or What!?!
I'm struggling to find what my optimization and constraint is. I've been told the cylinder has to have volume V and I need to know the shape of the can that is the most efficient cost and cost is equal to $1/per square cm. Would my optimization be the minimal cost of the can? Shape of the can is my constraint?
If we check this with the second derivative test, we find that the test is negative (plugging in the critical point we found for 'r'), meaning this is not a minimum but a maximum?
very helpful video! now to find the height that would minimize the amount of material for the cylinder or can used would I just plug in the radius I got as the final answer into the height equation??
Using your solutions ..The ht is twice the radius ...h= 10.8 .,,,,.r= 5.4Will the height always be twice the radius when it asks for dimensions that minimize Surf area of a cylinder?
Exactly the same way, except that when you use the first derivative test to investigate your critical point, your critical point will turn out to represent a maximum instead of a minimum. :)
integralCALC yeah it sounds so darn easy, till the exam actually comes and kicks me right in the ass by surprise. When that happens i usually forget everything. my theory is, if i picture your face before the kick, ill probably retain what you said :D
question: I am doing one right now thats the same question except the cylinder has no top. Would I simply subtract (pi)r^2 from the optimization equation or is there more to it then that?
Sorry for a noob question but i find it confusing to know if it is minimized or maximized. Isn't also maximized because the first derivative whether its max or min is 0? Or for those kinds of problems, is maximizing can't occur? Thank you for anyone who can answer
lmao 2 yrs later... to determine if it's max or min we do a second derivative and find the r-value, if the value is greater than 0 then it's minimum, if it's less than 0 then it's maximum
Very helpful video! But are the measurements for radius and height in cm or inches? Doing a project that requires a literal construction of the container
I had to learn this for my engineering degree, and I just want to say that you explained this so beautifully. Amazing.
Thank you so much! Glad it was helpful! :)
You're so welcome! Glad you liked the video. :)
Thank you!!!! You just saved me so much! I was in a time crunch, and your video was concise, easy to understand, and visually appealing. You have my neverending gratitude.
Thank you soooo much! This is the most helpful video I have ever watched in my entire life. I hope everything in your life goes right for you. Thank you!!!!!
Thank you so much, Brooke! I'm so glad the video helped! :D
that good feeling you get after you plug the numbers back in to double check, and your answers are right!
Still liking and replying to comments after 8 years. Amazing. Thank you for the help!!
You're welcome, Garrett! I'm so glad the videos are helping, and I'll always try to get back to as many people as I can! :)
The equation you find for A' is the equation that models how fast the surface area of the cylinder is changing as the radius changes. For example, if you want to know how fast the surface area is changing when the radius is equal to pi, you would plug pi in for r into the equation for A'. If the value you get back is positive, then this is how fast surface area is increasing at r=pi. If the value you get back is negative, then this is how fast surface area is decreasing at r=pi. :)
I know this is a late comment, but I had this type of question come up on my math homework and I don't remember the teacher explained this during class. I found your video and it was so helpful! Thank you so much!
You're so welcome, I'm so glad the video helped! :D
I fully understand now, thank you :D Feeling ready for my exam. This was the only chapter I struggled in
I always found it helpful as well, so I do my best to include them. :)
Thank you so much, also random but until watching this video I didn’t realize how nice it is to see a woman explain math. Idk it made me feel really happy!
For those just rote learning that they should differentiate - here is little intuition: since the relationship between radius and area is parabola, dA/dr = 0 is either maximum or minimum. But the graph has no maximum - you can increase the radius up to infinity and the area will just keep on increasing. So this means when dA/dr is 0, we have the lowest point of the graph and that is the radius with lowest area. Simple yet genious application of calculus.
Great explanation!! It only occurred to me recently that there ought to be a formula for minimizing the surface area of a cylinder, both to reduce construction costs, but also to limit radiation heat loss or gain. Moreover, the height to radius should be ratios, scalable to any size. I love geometry and trig, but never a big fan of calculus. Thanks for a fairly intuitive explanation. I was planning on using a spreadsheet for trial by error or range.
Clearly the best. Where were you when I needed you at the beginning of the semester? Thank you so much, your very helpful. Keep up the good work.
Best video on this topic available on youtube. Many thanks!
Thank you very much!
That makes me so happy! Glad I can help! :)
Thank you for posting this. Your explanation was very clear and I was able to follow along so I could get my project done.
You're welcome! So glad I could help. :D
how could you dislike this video is the only puzzling thing about it... Thanks alot for the post it's always really helpful :D
Thanks! I'm so glad I could help!
Brilliant explanation - thanks
i divided both sides by 4. since that gives me 0/4 on the left side, i just have 0. i get 4/4 on the right side, which just leaves me with 1. the r^2 disappears when you take the cube root of both sides. :)
Why is the 2000 become 500?
Thank you very much for your video. I was able to help my nephew with his homework with your help :)
Thank-you so much from Year 10 Aussie students.You are awesome,Krista!
I had to learn this for my interior design course ❤️❤️
Mam your way of teaching is quite easy and effective..thank u
You're welcome, Sheharyar. :)
So glad I found this video! Gonna ace my midterm this week now!
+Jennifer Stafford Awesome! Good luck on your midterm, I hope it goes great!!
Thank you again!!!!!! May God Bless You!!
This morning I was trying to remember how to work this problem out (I am in my sixties) and came across your video.
Thank you.
So:- Expanded out: r= (approx) 5.41926, h=(approx) 10.8385, d=2*r = (approx)10.8395.
So maximum volumn for min surface occurs when height = the diameter.
this... HELPED MEEEEEEEEEEEEEEEEEEE!
I knew how to do the problem, but I didn't know why I did the problem. now I know WHY!
You're welcome!
omg you just helped me with my homework! tysm
I was here, you just didn't know about me yet, lol!! I'm so glad it's helping!! :D
Glad I could help! :)
Your good thank you a lot first semester of calculus is the hardest. Atleast that's what people that took calculus in my High School say.
You're welcome! :)
Absolute legend thank you for this
Wow, this is the exact video I needed. Thank you!
You're welcome! I'm glad it could help!
Great vid! Helped me conceptualize the process soooo much better!
I'm so glad it could help!
you explain things wonderfully
Thanks!
i believe that DJ khaled once said about this page and I quote: "You Smart. You Real Smart. Matta fact baby you's a genius." #keystosuccess
Thanks again, for another very helpful video! I have improved my grade and calculus skills because of you, you are awesome!! Keep it up!!!
why does the square cancel out instead of the R? 4:50
Muchas Gracias, todo se puede lograr. Amo la Ciencia y la Tecnologia, Siento que todo se puede lograr con tus Clases. Gracias Maestra por su tiempo. ES POSIBLE. Matemáticas un gran misterio.
You're welcome, I'm so glad you're enjoying the videos!
this video was really helpful thanks Krista
Awesome! Glad it could help!
Great video!!! Thanks for your help ma'am
Thank you for this! Was just talking about this concept with my son (high school). He's excited about taking calculus soon. You're an excellent instructor 🙂👍
So glad it was helpful, Albatross! Good luck to your son on starting calculus! :)
For some, it certainly can be the most difficult. Glad I could help. :)
This is fantastic thank you so so much.
:D
you helped me ace my calc final
This video is absolutely brilliant and taught me exactly what I needed to know! 👏
Oh good! I'm so glad it was helpful! :D
Extremely helpful. Thanks.
Interesting tutorial. Thank you very much! Keep it up.
Hello, can you please explain why the exponent is -2? At 5:35
it's a basic principle of differentiation, you multiply the coefficient/constant by the exponent and subtract 1 from the exponent, and -1×2000=-2000 r^-1-1= -2
This just helped me on my HW! Thank you so much!
Awesome!
That was so helpful! Thanks!
This video was very helpful! Thank you!
Thanks a lot....its been a great help
You're welcome Ankur, I'm so glad it helped! :)
very easy explanation. Thanks a lot
You're welcome, nagesh, I'm glad it helped!
Love your videos! They seriously are a huge help...Thank you so much!
+Bill Hill You're welcome, I'm so glad they're helping!!
Thank you so much for your clear explanation. It helped me alot
+Faruk Karagoz You're welcome, I'm so glad it helped!
hi i have a question im confused at 7:09 how you went from 2000 to 500 cause im trying to substitute my question into your working if you get what i mean so right now im at (0= 4 pi r3- 750/ r2 ) sorry if this doesn't make sense
thank you 🙏🙏🙏🙏
you are the best. Thank you so much, seriously.
You're welcome!!
This really helped thanks
You're welcome, Noob, I'm so glad it helped! :D
I love you and your lecture
Would also be interesting to show in the conclusion to the video that area is minimized when h=2r (when the height of the cylinder equals its diameter). Just an interesting observation.
Thank you very much 😃
You're welcome, Syazwana! 😊
This is so accurate! Thank you so much 😊😊
You're welcome, Cathrina, I'm so glad it helped! :D
what does the can look like with the minimized surface area with its original volume. How is it gonna be different from the original shape of the unoptimized can?
thanks babe just did my homework for me.
you are the Best. I don't even know your name but you are the best.
Krista :)
integralCALC lol Thank you Krista What a beautiful name! You are the smartest and nicest You helped me pass my exam yesterday I'st that awesome Or What!?!
this was sooo helpfullllll bless you
The exact video I was looking for. Thank you so much for your help! From Fargo, North Dakota (:
Exactly what I needed too from Grand Forks, ND lol. #FightingSioux
Really good video. Thanks!
I'm struggling to find what my optimization and constraint is. I've been told the cylinder has to have volume V and I need to know the shape of the can that is the most efficient cost and cost is equal to $1/per square cm.
Would my optimization be the minimal cost of the can? Shape of the can is my constraint?
Beutiful an excelente explanation. Whatbis the tool you are use , it is great
awesome! i'm so glad to hear you did well... congratulations!! :)
Just love helping. :)
Thanks. I finally understood my assignment @_@
Awesome! I'm so glad I could help. :)
Thank you so much! If I were to solve for the maximization of the surface area, would the procedure be the same?
How do u solve for the max surface area
If we check this with the second derivative test, we find that the test is negative (plugging in the critical point we found for 'r'), meaning this is not a minimum but a maximum?
thank you so much!
very helpful video! now to find the height that would minimize the amount of material for the cylinder or can used would I just plug in the radius I got as the final answer into the height equation??
Hey, how would you calculate this for when the volume of the cylinder is an unknown value?
I was wondering what was the working out between the simplified area and area prime. how was the derivative formed from the equation before?
Thanks. I'm sure that I got this answer right on my test. Are you a mathematics major and teacher? Or do you just love helping people in math?
Using your solutions ..The ht is twice the radius ...h= 10.8 .,,,,.r= 5.4Will the height always be twice the radius when it asks for dimensions that minimize Surf area of a cylinder?
No, it won't always be that way. The height to radius ratio, or vice versa, can take on any value, not just this specific one. :)
so what's the unit for h and r?
Could someone recommend a video or website where I can learn how she found the derivative, A prime? Thanks!
I actually clicked like on this video before it started. I'm that confident it'll be good!
What if you were asked to maximize the cost of the metal? how would you do it?
Exactly the same way, except that when you use the first derivative test to investigate your critical point, your critical point will turn out to represent a maximum instead of a minimum. :)
Thank you it really help..
Awesome! You're welcome. :)
integralCALC
yeah it sounds so darn easy, till the exam actually comes and kicks me right in the ass by surprise. When that happens i usually forget everything.
my theory is, if i picture your face before the kick, ill probably retain what you said :D
Thank you
You're welcome!
thank you so much
question: I am doing one right now thats the same question except the cylinder has no top. Would I simply subtract (pi)r^2 from the optimization equation or is there more to it then that?
Nope, it's as simple as subtracting (pi)r^2 from the surface area equation, like you said. :)
Thanks
Sorry for a noob question but i find it confusing to know if it is minimized or maximized. Isn't also maximized because the first derivative whether its max or min is 0? Or for those kinds of problems, is maximizing can't occur? Thank you for anyone who can answer
lmao 2 yrs later... to determine if it's max or min we do a second derivative and find the r-value, if the value is greater than 0 then it's minimum, if it's less than 0 then it's maximum
8 years and it still relevant
Math is math.
Very helpful video! But are the measurements for radius and height in cm or inches? Doing a project that requires a literal construction of the container
+Patrick Wiley This problem is done in cm (metric units).
great vid!!