Maths Revision

[Callum]

I'm trying to do some last-minute math revision, as I have a test on Monday, and I found a question I can't do. And the mark-scheme doesn't make sense.

The question:

f:x |-> 3^x

Find the solution of the equation f''(x) = 2

My first step was to find the inverse of f(x)... f'(x)

So I let k = 3^x
ln(k) = ln(3^x)
ln(k) = x(ln(3))
x = (ln(k))/(ln3)
(x = log(base 3)(k))

But then I tried finding the inverse of the inverse... f''(x)and got the original function.

The answer scheme, however, says that f'(x) is not what I got at all, but is actually (3^x)(ln(3)).

What am I doing wrong?

[Seraph]

Well I'm not actually sure what you mean by inverse, what are trying to do with it, or why it would help you get f'(x). You are however correct that x = log(base 3)(k), but I would say that should be obvious from the initial problem, as it is basically the definition of a logarithm.

Here is how I would figure out f'(x) and f''(x):
f(x) = 3^x
f(x) = e^(x * ln(3))
f'(x) = d(e^(x * ln(3)))/dx
f'(x) = e^(x * ln(3)) * ln(3)
f'(x) = 3^x * ln(3)
f''(x) = d(3^x * ln(3))/dx
f''(x) = d(e^(x * ln(3)) * ln(3))/dx
f''(x) = ln(3) * d(e^(x * ln(3)))/dx
f''(x) = ln(3) * ln(3) * 3^x

[ 06-04-2005, 01:58 AM: Message edited by: Seraph ]

[Callum]

Dammit! That's where the problem lies! I knew I was forgetting something... f'(x) doesn't mean the inverse of x, it means the derivative of it!

D'oh!

Thanks!

[ 06-04-2005, 02:04 AM: Message edited by: Callum ]

[Aragorn1]

and f''(x) is the second derivative

f-1(x) is the inverse i think.

[Callum]

Yeah... bodes well for monday's exam no?

[Aragorn1]

Originally posted by Seraph: Well I'm not actually sure what you mean by inverse

the inverse is 1/f(x) and onviously, doing 2 inverses would be 1/1/f(x) which =f(x), hence it got Callum nowhere [img]smile.gif[/img]

[ 06-04-2005, 08:21 AM: Message edited by: Aragorn1 ]

[Kynaeus]

Please tell me this is not Grade 10 math!! :'(

my math exam has been very easy so far, 25 minutes for 15 multiple choice questions [img]smile.gif[/img]

[Aragorn1]

Originally posted by Kynaeus: Please tell me this is not Grade 10 math!! :'( my math exam has been very easy so far, 25 minutes for 15 multiple choice questions [img]smile.gif[/img]

I'm in the 'year 13' although we wouldn't call it that. I'm at college, so i'm a second year. I think it used to be called 'upper-sixth,' but only the oublic schools call it that now i think.

[Callum]

Maths multiple choice!?

*blinks*

Wow.. Sounds... difficult.

And I'm in the year below Aragorn1... though we do call it year 12/13 here.

[Aragorn1]

Originally posted by Callum: Maths multiple choice!? *blinks* Wow.. Sounds... difficult. And I'm in the year below Aragorn1... though we do call it year 12/13 here.

Does your school go from yr 7-13?