📦 Optimization Problem #5: Maximizing the Volume of a Box from a Square Material 📦

Optimization Problem #5: Maximizing the Volume of a Box from a Square Material

📦 Discover How to Maximize the Volume of a Box! 📦

In this video, we tackle Optimization Problem #5, where we aim to find the maximum volume of a box created from a 2ft x 2ft square piece of metal. By removing equal-sized corners and folding up the sides, we explore the process of optimizing the box's volume.

What You’ll Learn:

Understanding the Problem: Get a clear overview of how the box is formed from the original square material.
Setting Up the Volume Equation: Learn how to express the volume in terms of the size of the corners being cut out.
Applying Calculus: Follow the steps to find the derivative, determine critical points, and identify the maximum volume achievable.

Why Watch This Video?

Great for Students: Ideal for high school and college students looking to strengthen their understanding of optimization in calculus.
Clear Explanations: Enjoy step-by-step guidance that simplifies complex concepts and helps you grasp the optimization process.
Real-World Applications: Discover how these optimization techniques can be applied in various fields, from engineering to manufacturing.

📈 Don’t Forget to:

LIKE this video if it helps you understand optimization!
SHARE with classmates or friends who are eager to learn!
SUBSCRIBE for more math tutorials, problem-solving strategies, and educational content!

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[tulipbaby]

Oh my gosh! I was so confused on optimization problems, and I have my calculus final tomorrow. I'm starting to get more clearer on them thanks to your videos!! Thank you so much! :-)

[ghty]

So I loaded this video up this morning, but had to leave to go take my calc final before I had time to watch it. There was 1 question on my final that I couldn't figure out and it was literally the exact same question as in this video... fuck my life. 

[hotygirl]

I watched your videos last night because I had no idea how to do problems like this or how to use the chain rule but you make it so understandable. I felt really confident with my Calculus exam today.

[alisquin]

Thanks Patrick, this helped a lot for understanding the concept. Now only if there were a video for the 100s of other types of problems, I swear Optimizing has to be the most annoying sub chapter in all of 12 Calc.

[user]

5:30 lol brain fart, just proves how hard we rely on memorizing our time-tables instead of intuitively computing them. Thanks for the vid!

[annonymous]

right there, at 2:12 i stopped to give you a thumbs up. Seriously patrick, you're really gifted at this teaching thing.

[isaiahkirk]

Gosh, I'm so thankful for this video! I'm a Computer guy, and this in Cal 3 was burning me out!

[jetswhiteout]

No worries, 3 times 4 is a lot harder to figure out than calculus. Like these problems are nothing compared to 3 times 4 lol

[miguelquinonez]

Thank you. I just passed the cset subset 3. I’ve never taken calculus but I watched all your tutorials and they helped me a lot. I studied for about 200 hours Thank you.

[acmbhs]

dude you save my life literally every time i have to do any calculus work. my prof is a total dbag so luckily i have you to teach me. thanks a lot man

[michyswaga]

Times like this I just wonder how previous generations did it, without help from the internet! Thanks to channels like these and other free resources! Graduation in a month and I owe it mostly to u guys Khan Academy You Tube Google patrickJMT

[patrickjmt]

@Spacexchild super happy that i could do that for you : )

[SmittyKat]

Glad to see that someone who loves math as much as you do still has little brainfarts about simple stuff like the multiplication. I do this sometimes and it's like wtf I KNOW THIS lol. Good to see someone else does it.

[deborahafobunor]

And just like that I think I have found my new Calculus professor. Thanks!!! For some reason optimization always confuses me but now I feel more confident about it.

[AceAites]

"Unless youre a bad box builder !!!" LOL. Good sense of humor.

"What is 3x4? hmm whats 2x4..Wait what am i doing ? 3x4 is 12" LOL thanks so much for making these videos, even if it was super early in the morning, when you're not quite awake yet. This means a lot to us Calc students. :)

[samzuckerman]

Can't have 0 or 1 as values for x, the values can be in between but not inclusive:
0<x<1...If x were 0, the height of the figure would be 0 and that is impossible. Of x were 1, the length and width would be 0, which is also no longer a box.

[KylelovesMETAL]

My calculus final is tomorrow, and I have an A in the class and no real trouble with it. However, your videos make an awesome review. Thanks man, keep giving nerds a good name :p

[afdelgado]

You sir... are my tutor/helper/Nerd god. Your videos have helped me understand Calculus to the MAX!

[anastasiaanautodidact]

OMG CALCULUS IS STUPENDOUS (as much as how amazing your explanations always are)

[jnilknarf]

Haha I love how you just fly through taking derivatives and doing complex optimization problems, but then you hit 3x4 and get stumped for a minute. =). Great video btw, helped alot.