/sci/ - Science & Math

[Anonymous No.7526398]

why do people even use the derivative for optimization? cant we straight up jump to 2nd, 3rd, 4th (the biggest possible one given the equation) to avoid getting trapped in locals?

[Anonymous No.7526401]

>>7526398
Sage goes in options field.

[Anonymous No.7526405]

>>7526401
it was an unfortunate choice of picture, but the question is serious

[Anonymous No.7526437]

>>7526398
because there is no condition on the 2nd, or 3rd or 4th derivative that can indicate a candidate for an optimal point.

You first find points of interest with the first derivative, then you study them using the second derivative (or the second order differential if you have several variables)

[Anonymous No.7526443]

>>7526437
f(x) = x^3
f'(x) = 3x^2
f''(x) = 6x

what do you mean no optimal point candidate
make it so 6x = 0

[Anonymous No.7526487]

>>7526443
so what ?

f(x) = x

f''(x) = 0

make it so f''(x) = 0
now study all points in R.
Fuck off I know you're trolling so this is my last post in your shit topic.

[Anonymous No.7526495]

>>7526487
obviously
I get my kicks out of a pedantic mathematics question

if I was trolling, I would be posting in the IQ thread your heading towards

how about you get off your high horse and give an example/explain why I am wrong? Im trying to understand derivatives on a deeper level and your shitting on me to reply to some actual pseudo science thread on fucking elon musk or IQ

so go fuck yourself asshole

[Anonymous No.7526522]

>>7526495
I just gave you an example.
The first derivative is the most interesting because of the following theorem :
if f is differentiable on an open interval, and if f reaches a local extremum at a point x0 in that interval, then f'(x0) = 0.

[Anonymous No.7526567]

>>7526522
no I mean

lets say for example
quadratic

there can be multiple
f'(x) = 0

but only one global f''(x) = 0

so I say why dont we just straight up use f''(x) only and not worry about f'(x) when optimizing quadratics?

-and rinse and repeat for higher dimensions

[Anonymous No.7526569]

>>7526495
as soon as you go "you're not helping me the way i want to! fuck off!" you dont deserve anything

[Anonymous No.7526576]

>>7526569
>accusations of trolling/blatant ignoring
>vs
>helping but in alternative ways

[Anonymous No.7526585]

>>7526567
ok but it still doesn't work.


For example, f(x) = (x-1)^2
f'(x) = 2(x-1)
f''(x) = 2 (it's not even 0)
and f'''(x) = 0 for all x
so it never works actually.

[Anonymous No.7526611]

>>7526585
shit

[Anonymous No.7526614]

>>7526585
what about now?

[Anonymous No.7526627]

>>7526614
then take (x-1)^2(x+1)^2 = (x^2-1)^2 = x^4-2x^2+1
f'(x) = 4x^3-4x
f''(x) = 12x^2-4
f'''(x) = 24x
f4(x) = 24

use f''(x) then.
f''(x) = 0 means 24x = 0, or x = 0

while it's true that this give ONE extremum (the one at x=0), it doesn't give the other two (at -1 and 1)

you can choose to ignore what I already told you.

[Anonymous No.7526637]

>>7526567
>lets say for example
>quadratic
>there can be multiple
>f'(x) = 0
wtf?

[Anonymous No.7526687]

>>7526637
Im sick and half lucid trying to wrap my head around math, calm down
>>7526627
sorry Im not a mathematician but I see your point