Calculus 1: Max-Min Problems (28 of 30) Find Shortest Rope

In this video I will find the shortest rope that can be anchored on the ground between 2 posts (6ft and 8ft) 10ft apart.

Next video in this series can be seen at:

[tarikb]

thank you Michel, my hero. U provided me with the best knowledge in such a short amount of time. HOW IS THAT POSSIBLE??? I don't understand how such a miracle can come into this world at the palm of my hand. Thank you for everything, and I MEAN everything. Your cool swagger and your rocking bowtie can never be replaceable. I hope you're having the best day right now. Keep up the good work. From, your biggest fan, Tarik.

[ptyptypty]

an interesting result from the final answer is this: once you know "X" .. you also know d- x .. and knowing h1 and h2.. you have two side of the two Triangles... guess what?.. now you can find the value of the Angles formed by the two Ropes where they meet the ground.. Using the Tangent.... guess what again?.. lol... it turns out that those angles are always Equal!!.. amazing result!!... the same applies to the Two Light Sources in your other video... Math is SO COOL!!! thanks Michel!!

[johncarlovinluan]

your truly a nice and wonderful guys i will recommend you in my friend that like me having hard time in this kind of problem im glad that i found your video thanks a lot you give me idea how to solve this kind of proble and again thank you

[vevyovi]

man you could just say that L1 L2 must be linear when symmetry of L1 is taken and then you will get 14-10-x triangle

[fcar]

You truly have a gift for teaching  !  You make  Calculus easier to  understandthan anyone on the web ...Thanks for taking time to share  your vast  knowledge of Calculus ....and so many other subjects ...with so many many of us fortunate youtube  viewers out here. CT-fred

[juullibee]

thank you so much for this, this was genuinely so helpful and you explained everything very well!! <3

[michaelempeigne]

6 / r = 8 / ( 10 - r )
60 - 6r = 8r
60 = 14r
r = 60 / 14
r = appr. 4.3

[waynehan]

I see this video along with other videos/articles, but i have one question. This is the way to find a local extrema, and i know that. The point is, how do we confirm it's a local minimum(not maximum)? This requires the second derivative of the formula, and I found it very clumsy. However, ignoring that completely is simply not acceptable in mathematics. Math is all about complete(self-contained), precise and accurate.
Honestly this type of question can be solved so easily by geometry, but i guess we want to apply AP calc here. Therefore, my question still stands, waiting for an answer.

[rickymarzan]

Thank you very much sir. I learned a lot to your video. Godbless.

[justinya]

Awesome video! Keep up the great work!

[povhengyam]

Well, I did it right and I throw my paper away before seeing this video. :(