Question

have no idea where to start on this :(

attached inside!!
thanks!! :D

Answer 1

x=__________

Answer 2

You have the word "minimize" there.

A good way to start is differentiating the function.
Go ahead now :P

Answer 3

okay:)

ermmmm

\[U' = \frac{ b(x-2a) }{ x ^{3} }\]

Answer 4

oh wait oops

Answer 5

is it this? \[U' = \frac{ ab(x-2a) }{ x ^{3} }\]

okay umm i think i got it right (almost right? haha) this time :/ what do you think?

Answer 6

Okay, a few things we note.
One, x cannot be zero.
You can see why, right?

Answer 7

ermm i think so....

it's because of the x^3 right?

Answer 8

x^3 in the denominator...
anyway, we have to get a minimum, so the derivative, which you have just acquired, is set equal to zero.

Do that, and find x.

Answer 9

you end up doing this right?

multiply both sides by x^3

you get

ab(x-2a)=0

divide by ab

x-2a=0

x=2a

?

Answer 10

There you have it :)

Answer 11

That's the ONLY value of x that gives you a zero derivative, right?

Answer 12

Anytime you need to maximise or minimise some function, think *derivative* ok? :)

Answer 13

yes:)

ohh so my answer will be 2a ? :O

Answer 14

That's right :)

Answer 15

--because to maximise or minimise a function, the derivative has to be zero (or not exist, but more on that some other time)

Answer 16

okay yay!

and will remember to think derivative :)

sometimes, i just get the fractioned derivatives mixed up haha but i just need to practice more!! :D

ahh okay:)

thank you!! :)

Answer 17

Need to sign off now, hopefully any further questions will be easy for you.
----------------------------
Terence out

Answer 18

haha okay:) thanks!! see ya later! :D