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To find f
you need to first find f'
the find f' given f'' integrate both sides

hmm.. \[f'(x) = \frac 1x + c\]
??

almost

you are missing a certain constant multiple

ahh \[f'(x) = -\frac 1x + c\]

or maybe i should do it \[f'(x) = -\frac 1x + c_1\]

i might have typoed

integrate again

ah yes i did. it's f'(2) not just f(2)

get a system of 2 eau and 2 unknowns

hmm \[f(x) = -\ln x + c_1 x + c_2\]
yes?

ok great.
you can find that constant by using f(1)=0
and then do what zarkon says to find f

you can do the problem with two given values of f

or you can wait to find the first constant whatever

i suppose x > 0 is just there to note that -ln x exists?

f'(2) = 0
so f'(2) = -1/2 + c_1 = 0
does this mean c_1 is 1/2?

yes adding 1/2 to both sides solves that equation for c_1

then f(1) = -ln (1) + 1/2 x + c_2 = 0
so c_2 is -1/2?

x is 1
so you have -ln(1)+1/2(1)+c_2=0
and yes

oh. yeah...forgot to sub 1 into x the second time

so \[f(x) = -\ln x + \frac 12 x - \frac 12\]
??

tep

nice. thanks

i just noticed this was my 1000th question