liizzyliizz
  • liizzyliizz
find the equation of the tangent line to the curve f(x)= lnx/e^x at x=1
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
slope m=f'(1) point (1,f(1)) equation: (y-f(1))=m(x-1)
TuringTest
  • TuringTest
^right, so what have you got for f'(x) ?
liizzyliizz
  • liizzyliizz
wouldn't f'(x) be (1/x - ln(x)) * e^-x ?

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TuringTest
  • TuringTest
yeah, so what is f'(1) ?
liizzyliizz
  • liizzyliizz
it would be 1
liizzyliizz
  • liizzyliizz
?
TuringTest
  • TuringTest
\[f'(x)=e^{-x}(\frac1x-\ln x)\]\[f'(1)=e^{-1}(\frac11-\ln 1)=e^{-1}(1-0)=e^{-1}\]
liizzyliizz
  • liizzyliizz
err I messed up on the e^-1 :/
TuringTest
  • TuringTest
so that's your slope, m what's f(1) ?
liizzyliizz
  • liizzyliizz
0
anonymous
  • anonymous
right, so now you have: slope m=e^-1 and point (1,0) replace in the equation
liizzyliizz
  • liizzyliizz
ok so it would be y-0=e^-1(x-1) correct?
liizzyliizz
  • liizzyliizz
then you would just change the form, which is what im doing now to match the choices in my question
TuringTest
  • TuringTest
yeah that's right don't know what for you need it in...
TuringTest
  • TuringTest
what form*
anonymous
  • anonymous
y=e^-1(x-1) is the equation of the tangent line to the curve
liizzyliizz
  • liizzyliizz
these are the choices- x-ey-1 =0 x+ey-1=0 x-y-1=0 ex+y-1=0 ex-y-1=0
liizzyliizz
  • liizzyliizz
i feel like when i took this test i did the work somewhat right, but when it came to switching it out i made a careless mistake so i want to know which one was it. :c
TuringTest
  • TuringTest
multiply both sides by e I meant :/
TuringTest
  • TuringTest
actually something is missing...
TuringTest
  • TuringTest
\[\large y=e^{-1}(x-1)\]\[\large ey=x-1\]\[\large x-ey-1=0\]but that's not a choice...
TuringTest
  • TuringTest
oh, it is the first one I didn't see that one on the first line
anonymous
  • anonymous
liizzyliizz the first choice is -x-ey-1 =0? or x-ey-1 =0?
liizzyliizz
  • liizzyliizz
first choice is x-ey-1 =0
anonymous
  • anonymous
that is the answer
liizzyliizz
  • liizzyliizz
well this helped thank you, I know what I did wrong. *sigh*

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