Minimising Without Calculus

[@txikitofandango]

Once you said the magic words "complete the square" it was a big enough hint for me. Very cool! Will definitely remember this idea

[@vladimir10]

Simple, yet still possess the magic of math in all its glory! Thank you for the video! Waiting for them every Friday which makes weekend better!

[@DrBarker]

Thank you, glad you enjoyed it!

[@robertsandy3794]

Listening to the video, it finally struck me that you didn't say "zee" but zed! Thanks from Australia!

[@Utesfan100]

I have become convinced it becomes a zed when you cross it.

[@picrust314]

That is great, but I still wonder if he uses the long scale (milliard, not billion)

[@kwiky5643]

Like in France

[@user-wu8yq1rb9t]

Hello dear Dr Barker (the beautiful mind) Just on time as always Thanks

[@DrBarker]

Thank you, good to see that you're still following the channel!

[@Nibor999]

Nice work!

[@paradoxicallyexcellent5138]

Is there any interesting insight to be gained from thinking in terms of the symmetric matrix of coefficients of the terms? This algorithm you presented certainly seems to work well enough. I am going to bet a beer the eigenvalues have something to do with whether the function has a min or max or saddle.

[@KrishanKucheria-wl8ug]

Innovative solution! How can we generalise this for any coefficients and if any yz, x, y, or constant terms are present?

[@louisrobitaille5810]

1:06 I was so confused for a second because I thought "5x^2 + y ^2 + 2z^2" and "-2xy + 4xz + 6z" were two different expressions. Perhaps you could write such expressions in a single line in the future, or at least make it very clear that's a single expression? Thanks in advance 😅.

[@ayushrudra8600]

How would you solve this with calculus ?

[@DrBarker]

The standard approach would be to take partial derivatives to look for maximum/minimum points. So differentiate everything with respect to x only, keeping y & z fixed, then set ∂f/∂x = 0. We would do the same to set ∂f/∂y = 0 and ∂f/∂z = 0, then solve these 3 simultaneous equations to find values of x, y, z which minimise the function.

[@trumpgaming5998]

Does a similar approach work with lagrange multipliers

[@ultrio325]

could this question be solved via the AM-GM inequality as well?

[@sr6424]

A question- this worked magically well with this set of values. Will it work as well with other sets of values?

[@glebyakovlev1321]

of course not in general, differentiate

[@ConManAU]

If you just change the coefficients of the terms that appear in this expression, then the same kind of approach should still work. If you have extra terms, it takes a bit more work to figure out how to complete the squares. It can usually be done, though, if the whole thing is still quadratic.

[@glebyakovlev1321]

@@ConManAU зависит от реальной поверхности которая задаётся всякими членами второй степени и ниже с разными коэффициентами, ну может там гипербола на парабалу?

[@glebyakovlev1321]

@@ConManAU if the whole thing is still quadratic

[@ВасилийДрагунов-н8т]

it will, but it might have no minimal value depending on signs +- in front pf the coeficients

[@brendanward2991]

I thought it was easier using calculus. Partially differentiate with respect to x, then y, then z, giving three equations in three unknowns. Took about five minutes.

[@user-wu8yq1rb9t]

❤

[@chimmychonga4795]

Linear algebra come save us 😭

[@ImperfectKingdomSeeker]

Ok I'll minimize: You're a trivial problem. You're nothing.