06-04-2005, 01:29 AM | #1 |
Symbol of Cyric
Join Date: October 21, 2004
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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?
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06-04-2005, 01:51 AM | #2 |
Quintesson
Join Date: September 12, 2001
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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 ] |
06-04-2005, 02:03 AM | #3 |
Symbol of Cyric
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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 ]
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06-04-2005, 04:12 AM | #4 |
Symbol of Cyric
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and f''(x) is the second derivative
f-1(x) is the inverse i think. |
06-04-2005, 06:25 AM | #5 |
Symbol of Cyric
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Yeah... bodes well for monday's exam no?
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06-04-2005, 08:18 AM | #6 | |
Symbol of Cyric
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Quote:
[ 06-04-2005, 08:21 AM: Message edited by: Aragorn1 ] |
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06-05-2005, 12:12 AM | #7 |
Drow Warrior
Join Date: March 15, 2005
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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] |
06-05-2005, 05:24 AM | #8 | |
Symbol of Cyric
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Quote:
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06-05-2005, 06:19 AM | #9 |
Symbol of Cyric
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Maths multiple choice!?
*blinks* Wow.. Sounds... difficult. And I'm in the year below Aragorn1... though we do call it year 12/13 here.
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06-05-2005, 12:54 PM | #10 | |
Symbol of Cyric
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Quote:
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