Question

Differentiation problem

Answer 1

In the equation above, find an expression for the value of x that will optimise y.

http://tnypic.net/aba25.jpg

Answer 2

I know that I need to derive this, but I am struggling to derive this equation.

Answer 3

I broke the equation into 3 different terms. d/dx[a/b] + [a/lnx] + [a/(c/x)]

Answer 4

I don't quite now how to solve it, but it's easier to look at this way
\[y=\frac{a}{b+lnx+\frac c x}\]

Answer 5

*know

Answer 6

a b and c are constants so, I thought it would be easier to break the eqation into 3 smaller equations.

Answer 7

@ironictoaster.... i don't think you can do that...

Answer 8

Hmm, I'll try wolfram, see what they say.

Answer 9

try doing logarithmic differentiation...

since \(\large y=\frac{a}{b+lnx+\frac{c}{x}} \)

\(\large y=\frac{a}{b+lnx+\frac{c}{x}} \rightarrow lny=lna-ln(b+lnx+\frac{c}{x})\)

Answer 10

\[\frac{(denominator)*\frac{d}{dx}(numerator)-(numerator)*\frac{d}{dx}(numerator)}{denominator^2}\]
would this work @dpalnc

Answer 11

@MathSofiya , definitely....

Answer 12

\[\frac {(b+lnx+\frac cx)*(0)-a(0+\frac 1x-\frac{c}{x^2})}{(b+lnx+\frac cx)^2}\]

Answer 13

bump the question and see what other OS'ers have to add

Answer 14

It's causing me problems for the past 2 hours now, I'll have to ask my math lecturer.

Answer 15

Thanks for the help though!

Answer 16

No prob....I'm sure @Zarkon or @mahmit2012 are gonna jump in to help soon

Answer 17

or @KingGeorge

Answer 18

or @TuringTest

Answer 19

I think what you could do is try to minimize the denominator. Instead of maximizing the entire thing, look for the minimum of \[b+\ln(x)+\frac{c}{x}\]

Answer 20

I'll try that now, I'll find out the answer tomorrow and post it!

Answer 21

The derivative is \[\frac{1}{x}-\frac{c}{x^2}\]Set that equal to 0, you get \[\frac{1}{x}=\frac{c}{x^2}\implies x=c\]

Answer 22

Hence, if it does have a local maximum, it must be at \(x=c\).