Ex: Optimizing the Volume of a Box With Fixed Surface Area

[@viralgandhi5491]

Came down here at the comment section to talk about the cute helper James and found no one :( This Professor is indeed underrated!

[@colewalker2916]

YEAHH GET THE KID DOING SOME INTEGRALS!

[@DrTrefor]

Haha put him to work!

[@jonaslentfer2494]

Hey Dr. Trefor, Very informative, and a different expierence with calculus than what i was taught in school. I love the fact that you are stating the values of H and L in times of roots instead of simplified numbers, which then gives a more satisfying answer to our problem. I have always had a problem in understanding how exactly you are using algebra to simplify the expressions for H and L in respect to the square roots. Would you care to explain a bit deeper for me, or could you point me in the right direction in terms of videos you've made where I can learn a bit more of the complex algebra? Thank you so much for your video series, they are very valuable to me.

[@Alternative-Works]

What happens when the box doesn't have a square base as a given? Will the optimal volume always result in a square base?

[@klausnordmeyer]

I'm not clear about the infinite L endpoint reasoning at 7:16. If L goes to infinity, then H goes to zero. Why should infinity times zero be considered zero, rather than indeterminant? The "no volume" situation actually occurs well before L equals infinity due to the constraint of 12000 cm**2 of material, with L determined by equating the volume (after removing H) to zero. This would seem to be what actually allows us to determine that the volume would be zero at the right endpoint of L. Sorry if I'm nitpicking, these lectures are excellent. Although I do agree with another comment that it would be great to have a series of lectures that gave proofs for the calculus theorems.

[@slowfern]

Thank you helper james

[@johnnolen8338]

The method of Lagrange multipliers is much more efficient in this case.

[@mnada72]

Would it give the same answer if we differentiate with respect to H instead of L ?

[@DrTrefor]

Yup

[@LofuLammui]

Can I carry out second derivative test to show that d^2V/dL^2 = -3L/2

[@DrTrefor]

Yup 2nd derivative test works great too.

[@cutestbear3327]

one proud dad, and deservedly so :D

[@まつまつ-x1f]

Calculus for baby. Nice!

[@zuko2216]

There's l everywhere 💀

[@dannyBezos]

the chonkie kid must have grown up by now...sigh

[@DrTrefor]

He’s 7!!!