Optimization: Find Largest Area of a Rectangle Divided into Four Pens

This video shows how to find the largest area of a rectangle divided into four pens given the perimeter.

[@theapcalculustutor367]

Great Video! You make it very easy to understand and follow along with the problem. Keep it up!

[@crowsmathclass]

Thank you.

[@olivialiang7505]

Southern mathematician 🤠

[@dividale2821]

thanks, this helped me with the process of solving a similar question with different values instead

[@crowsmathclass]

You’re welcome. Glad it helped.

[@juliak5980]

3:49 wouldn't it be positive 4/5 since you added 4/5 to both sides?

[@crowsmathclass]

Yes. Brain must have slipped. The answer is correct though. Thanks for pointing it out.

[@MrRobot-jb5tl]

Just a suggestion, you can use the second derivative of the function to check if its a min or a max. If the second derivative is negative, the function is concave down, giving us a local max, if it is positive, the function is concave up and is giving a local min. In this case the second derivative would be: A'' = -4/5 So the second derivative is negative and is concave down for all values of x, meaning the function has only a local max

[@crowsmathclass]

👍

[@duckwifboots]

Helped me out! Thanks a lot.

[@crowsmathclass]

You’re welcome.

[@alancoronalopez8318]

Great video, thanx a lot

[@crowsmathclass]

Thank you.

[@alexsimpson4516]

BLESSSS THIS QUESTJON IS ON MY TAKE JOME TEST

[@crowsmathclass]

👍

[@tinovimbasemu4519]

How would we solve this if it just said maximize the area of the pens? Not total area

[@crowsmathclass]

That is just the total area divided by 4. To do just one pen they would have to tell you the amount of fencing for one pen and this information is not given.

[@tinovimbasemu4519]

@@crowsmathclass Great! Thank you for the quick response.

[@JDCrain]

Don't you mean -187.5?

[@edenisok894]

What is a derivative??? I don’t understand this

[@smowy9323]

W Steve Crow

[@speedytadpole7571]

would the answer be the same if there was 3x and 3y instead of 2x and 5y? so thers 4 squares same as yours

[@crowsmathclass]

Probably not. I would have to calculate it though. But I doubt it.

[@justins5756]

Sounds like Dave Ramsey!!!!!

[@crowsmathclass]

👍

[@hermes112]

god bless

[@crowsmathclass]

Thank you. Glad it helped.