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From: Fred Nurk on 9 Jul 2010 00:45
f(x) = -3ln(2 - x). If g(x) = x ^ 2, find, using calculus, the
coordinates of any stationary points of (f + g)(x).

I get ([2 - 10 ^ (1 / 2)] / 2, 3ln{[10 ^ (1 / 2) - 2] / 3} - 10 ^ (1 / 2)
+ 7 / 2)) but the answers say ([2 - 10 ^ (1 / 2)] / 2, -3ln{2 - [2 - 10 ^
(1 / 2)] / 2} + 7 / 2 - 10 ^ (1 / 2)).

Are they equivalent and if so, how?

TIA,
Fred
From: Gerry Myerson on 9 Jul 2010 01:53
In article <GPxZn.453$Yv.452(a)viwinnwfe01.internal.bigpond.com>,
Fred Nurk <albert.xtheunknown0(a)gmail.com> wrote:

> f(x) = -3ln(2 - x). If g(x) = x ^ 2, find, using calculus, the
> coordinates of any stationary points of (f + g)(x).
>
> I get (

>[2 - 10 ^ (1 / 2)] / 2,

>3ln{[10 ^ (1 / 2) - 2] / 3} - 10 ^ (1 / 2) + 7 / 2))

>but the answers say (

>[2 - 10 ^ (1 / 2)] / 2,

>-3ln{2 - [2 - 10 ^ (1 / 2)] / 2} + 7 / 2 - 10 ^ (1 / 2)).

> Are they equivalent and if so, how?

Well, the first ones are identical, so let's look at the second one
in each pair.

They both have -sqrt10 and 7/2, and a 3 out front, so let's
look at the rest:

log ((sqrt 10 - 2) / 3) versus

- log ( 2 - (2 - sqrt 10) / 2)

Now log A = - log (1/A) so the question is whether

3 / (sqrt 10 - 2) is the same as

2 - (2 - sqrt 10) / 2.

Can you take it from here?

--
Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Fred Nurk on 10 Jul 2010 05:55
Gerry Myerson wrote:
> <snip>
> ...so the question is whether
>
> 3 / (sqrt 10 - 2) is the same as
>
> 2 - (2 - sqrt 10) / 2.
>
> Can you take it from here?

Yes, thank you.

:)

Fred
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