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Calculus help (Optimization Integration)
Kyuande:
This is fake lol
Neventii:
what a loving cunt, I'll make sure to ban him from my education system
Ipquarx:
--- Quote from: Pastrey Crust on February 13, 2017, 10:49:01 AM ---1) Part the number 100 into two which the sum of their cubes is minimum.
--- End quote ---
Okay, so we have 1 variable here:
100 = a + (100 - a)
And we're trying to minimize:
a^3 + (100 - a)^3
In the domain [0, 100]
We get the derivative of this:
d/dx (a^3 + (100-a)^3) = 3a^2 - 3*(100-a)^2
Simplifies into:
600 (a - 50)
Find where this is zero, in this case a = 50. This is where the minimum is. I forget what theorem this comes from.
So your minimum is 250,000 for the sum of cubes.
Pastrey Crust:
--- Quote from: Ipquarx on February 13, 2017, 05:05:45 PM ---Okay, so we have 1 variable here:
100 = a + (100 - a)
And we're trying to minimize:
a^3 + (100 - a)^3
In the domain [0, 100]
We get the derivative of this:
d/dx (a^3 + (100-a)^3) = 3a^2 - 3*(100-a)^2
Simplifies into:
600 (a - 50)
Find where this is zero, in this case a = 50. This is where the minimum is. I forget what theorem this comes from.
So your minimum is 250,000 for the sum of cubes.
--- End quote ---
Aha, here's where I messed up
--- Quote from: Ipquarx on February 13, 2017, 05:05:45 PM ---d/dx (a^3 + (100-a)^3) = 3a^2 - 3*(100-a)^2
--- End quote ---
I wrote
--- Quote ---d/dx (a^3 + (100-a)^3) = 3a - 3*(100-a)
--- End quote ---
Punished Toxicology:
--- Quote from: Insert Name Here² on February 13, 2017, 10:52:17 AM ---I'll be sure to ban Calculus Help (Optimization Integration) from my server, thanks for warning us!
--- End quote ---
you are a comedy revolutionary