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find f
\[f''(x) = x^{2}, \quad x > 0,\quad f(1) = 0, \quad f(2) = 0\]
 one year ago
 one year ago
find f \[f''(x) = x^{2}, \quad x > 0,\quad f(1) = 0, \quad f(2) = 0\]
 one year ago
 one year ago

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myininayaBest ResponseYou've already chosen the best response.3
To find f you need to first find f' the find f' given f'' integrate both sides
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
hmm.. \[f'(x) = \frac 1x + c\] ??
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
you are missing a certain constant multiple
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
ahh \[f'(x) = \frac 1x + c\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
yes :) now to find the constant hmmm....you are missing a certain initial condition to do that .... your question doesn't make sense .... you need one of those to be f'(something)=another something
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
or maybe i should do it \[f'(x) = \frac 1x + c_1\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
i might have typoed
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
ah yes i did. it's f'(2) not just f(2)
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
get a system of 2 eau and 2 unknowns
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
hmm \[f(x) = \ln x + c_1 x + c_2\] yes?
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
ok great. you can find that constant by using f(1)=0 and then do what zarkon says to find f
 one year ago

ZarkonBest ResponseYou've already chosen the best response.1
you can do the problem with two given values of f
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
or you can wait to find the first constant whatever
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
i suppose x > 0 is just there to note that ln x exists?
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
oh wait.... i guess you can do it with f(something1)=another something1 and f(something2)=another something2 oops
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
f'(2) = 0 so f'(2) = 1/2 + c_1 = 0 does this mean c_1 is 1/2?
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
yes adding 1/2 to both sides solves that equation for c_1
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
then f(1) = ln (1) + 1/2 x + c_2 = 0 so c_2 is 1/2?
 one year ago

myininayaBest ResponseYou've already chosen the best response.3
x is 1 so you have ln(1)+1/2(1)+c_2=0 and yes
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
oh. yeah...forgot to sub 1 into x the second time
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
so \[f(x) = \ln x + \frac 12 x  \frac 12\] ??
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
i just noticed this was my 1000th question
 one year ago
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