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

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

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

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

myininaya Group TitleBest 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

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

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

Zarkon Group TitleBest ResponseYou've already chosen the best response.1
integrate again
 one year ago

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

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

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

myininaya Group TitleBest 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

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

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

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

myininaya Group TitleBest 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

lgbasallote Group TitleBest 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

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

lgbasallote Group TitleBest 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

myininaya Group TitleBest 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

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

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
nice. thanks
 one year ago

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