Optimization: Minimize Surface Area of a Box Given the Volume

This video shows how to minimize the surface area of an open top box given the volume of the box.

[@atlaszx6966]

studying for my ap calc final and optimization has been a bit rough for me, your video helped so much with how thoroughly you explain it that I can follow along. Thank you!

[@crowsmathclass]

You’re welcome. Glad it helped. Good luck on your test.

[@shuttlevfx1519]

These types of videos are everlasting. Thank you for this.
Started my optimization unit and this was extremely helpful.

[@crowsmathclass]

You’re welcome. Search my channel for optimization and you will find a lot of videos.

[@kaitlyncicatello4605]

This helped me SO much thank you. Explained everything perfectly. Thank you!!!

[@crowsmathclass]

You’re welcome. Glad it helped. Thank you for the comment.

[@towersj6132]

Thanks man! This was a life saver on my virtual calculus test!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@jfilipeneta]

Your explanations are from another world. I really understood where x and h were after the 7th time!

[@crowsmathclass]

Thank you.

[@gm9262]

Thank you so much!! You are a great teacher!

[@crowsmathclass]

Thank you.

[@zeddeas4182]

Thank you so much you just saved my lift on this quiz.... It was really helpful that you explained slowly as you went along :)

[@crowsmathclass]

You’re welcome. Glad it helped.

[@maximuscullan8649]

THANK YOU, you explained everything perfectly

[@crowsmathclass]

Thank you. Glad it helped.

[@sandrasorto8375]

You're a life saver. THANK YOU!!!!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@ilovebunnies04]

Thank you for your video! It was easy to undersand and the explaination was fabulous.

[@crowsmathclass]

Thank you. Glad it helped.

[@alexfelipe7679]

Thank you for the video it really helped me understand these types of problems.

[@crowsmathclass]

You’re welcome. Glad it helped.

[@77n0bu3]

This really helped me thank you so much 🙏

[@crowsmathclass]

You’re welcome. Glad it helped.

[@lycybin8347]

Helped me so much! Thanks!

[@crowsmathclass]

You’re welcome.

[@strawbeano]

omg this helped me passed my math CPT thank you so much

[@crowsmathclass]

You’re welcome. Glad it helped.

[@GSSingh]

That's wonderful way of explaing even a person without any knowledge of math and calculas will understand it.

[@crowsmathclass]

Thank you.

[@TheGameCritc]

have w lovely day! this helped me so much

[@crowsmathclass]

Thank you. Glad it helped.

[@wade4846]

Been behind on uni so watching these to catch up love the accent

[@crowsmathclass]

Thank you.

[@katkrasher]

So simple and amazing thank you

[@crowsmathclass]

You’re welcome.

[@AvaDuffy-uf8gu]

thank you! very helpful

[@crowsmathclass]

You’re welcome.

[@boitumelomhlanga537]

Perfect explanation 👌.

[@crowsmathclass]

Thank you.

[@alfredgomez5261]

hi just for clarifications while moving the 2x to the left side it should be negative right?

[@Lelo.Machaka]

Thank you you were so much help

[@crowsmathclass]

You’re welcome.

[@comfyDev]

Thank you!

[@crowsmathclass]

You’re welcome.

[@emmahonkanen4572]

THANK YOU SO MUCH

[@crowsmathclass]

You’re welcome.

[@user-mw6fh5oj2c]

thank you

[@crowsmathclass]

You’re welcome.

[@emanamjad505]

THANK YOU

[@crowsmathclass]

You’re welcome.

[@21506ash]

Thank you

[@crowsmathclass]

You’re welcome.

[@divine6600]

how does the 4x x the divided x^2 cancel

[@bnxpcapth2o445]

Ahh sorry the other one wasn’t the one I was originally looking at this is the one I am looking at would the volume be the same either way because a open top box and a closed top box can only hold the same amount of volume

[@crowsmathclass]

It would be different because we are minimizing surface area. The top would add more surface area.

[@nathanrao4500]

Thanks for the simple explanation. May I ask, though, how do we know we didn't find the maximum? Thank you!

[@crowsmathclass]

By determining if it is a relative max or min using the first or second derivative test. The way you do when you were graphing.

[@PerilGames]

tysm

[@crowsmathclass]

You’re welcome.

[@teetee-si1bw]

king

[@pattytheratty]

Legend

[@crowsmathclass]

👍

[@nicholasborelli275]

Do you have an example where all three dimensions are different? x, y, h?

[@crowsmathclass]

I don’t think so.

[@alexislee9727]

praise

[@crowsmathclass]

Glad it helped.

[@patrickschack358]

Isn’t the surface area expression supposed to be 2x^2+4xh?

[@crowsmathclass]

No. It’s an open top box.

[@matty2081]

What happens if its an open top rectangle?

[@crowsmathclass]

You just use area of bottom and sides.

[@Minji-hx3lo]

wheres the process to find the minimization?

[@IGReelsEnjoyer]

how about minimizing the surface area of a cuboid? S= (l*w)(2l*2w*4h*)?

[@crowsmathclass]

l=w=h

[@kristenmensah4890]

how did 64000 turn to 40?

[@Jake-sr1yb]

3rd root - or 40*40*40

[@dag.3r504]

When a cow boy teaches calculus:

[@crowsmathclass]

👍

[@liliannaortiz3592]

just had this on exam with no calculator???? i feel cheated because i had the right equations and process but couldn’t get definitive answer of the cube root of a 6 digit number. rip

[@crowsmathclass]

That sucks.

[@liliannaortiz3592]

just had this on exam with no calculator????

[@pepsiyummie1]

Yawns, burps…otherwise very helpful.

[@crowsmathclass]

Glad it helped.