Calculus help (Optimization Integration)

[Kyuande]

This is fake lol

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[Neventii]

what a loving cunt, I'll make sure to ban him from my education system

[Ipquarx]

1) Part the number 100 into two which the sum of their cubes is minimum.

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]

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.

Aha, here's where I messed up

d/dx (a^3 + (100-a)^3) = 3a^2 - 3*(100-a)^2

I wrote

d/dx (a^3 + (100-a)^3) = 3a - 3*(100-a)

[Punished Toxicology]

I'll be sure to ban Calculus Help (Optimization Integration) from my server, thanks for warning us!

you are a comedy revolutionary

[Insert Name Here²]

you are a comedy revolutionary

thank you ill be here all night

[Pastrey Crust]

Thanks Badspot.

[SetGaming]

Also how to correctly do integration by parts? I have this excersize which I obviously did incorrectly
1) ／ln(x^2) dx

Is this typed correctly? Is it:

Code: [Select]

integral of ln(x^2) dx ?

[Outland Predator]

What's his ID?

The answer to the question is the ID.

[TableSalt]

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[Outland Predator]

Beef Wellington?

[Ipquarx]

2) A prism's length is thrice the width and the sum of the length, width, and height is 60.
Calculate the maximum volume possible. \

Could you please re-phrase this... Is it a rectangular prism? If not, what kind? Also thrice the width of what? Figured that part out, I'm dumb

[Pastrey Crust]

Is this typed correctly? Is it:

Code: [Select]

integral of ln(x^2) dx ?

Yes, that.

Could you please re-phrase this... Is it a rectangular prism? If not, what kind? Also thrice the width of what? Figured that part out, I'm dumb

Rectangular prism. L = 3w L+W+H = 60

I got a negative answer for some reason. I started off with

w*3w*(4w-60)=0

[Luigi609²]

you should all do standup comedy

but we're all lonely cigarettes sitting down in front of a computer

[Pastrey Crust]

then do sitdown comedy duh