Question

Calculus-Optimization: The product of two positive numbers is 54. Fnd the numbers if the sum f the first number plus the square of the second number is as small as possible

Answer 1

malevolence u disappeared again lol your just giving me the answer and i dont understand

Answer 2

Okay from x+(54^2/x^2)=s.
Taking the derivative. What confuses you?

Answer 3

how u found the derivative of the 2nd part...

Answer 4

Okay. (i'm going to call 54^2=a, its easier to write)
Rewrite it as: x+ax^(-2)=s. Because a/x^2=ax^(-2).
Follow me up to that point?

Answer 5

yes

Answer 6

:)

Answer 7

Okay, then you have a power rule
d/dx(x^n)=nx^(n-1)
So: It becomes 1+(-2)a(x^(-3))=0. Right?

Answer 8

ok so we just pretty much ignore the 54...thats what confused me i thought since it was (54/x)^2 we would use the chain rule...no?

Answer 9

The 54 is just a constant, you can pull it out of a derivative. So its immaterial. (I just called it a for convenience).

Answer 10

You can use the chain rule. You would have (2)(54x^-2)(-1)(54/x)

Answer 11

Convince yourself that those are both equally valid. :P

Answer 12

ok...i'm sorry for my slow moment im very good with derivatives but...with optimization i dont know if i should multiply or which rule's i should use thanks so much lol

Answer 13

u think if i use the chain rule i would get the same answer?

Answer 14

Thats what I did above^^ Yes you will. If you multiply what I have together up there, you get the same thing.

Answer 15

oh ok THANKS SO MUCH..i dont know why im so confused with optimization

Answer 16

No problem, after you do it a bunch it'll become easy. :P Just post any questions you have and I'll try to explain a little better.

Answer 17

ok! thanks