Question

If f'(x) = 2/x and f(sqrt of e) =5, then f(e) =?

Answer 1

\[f(\sqrt{e})=5\]??

Answer 2

are you allowed to integrate? if so, then if
\[f'(x)=\frac{2}{x}\] then
\[f(x)=2\ln(x)+C\]

Answer 3

we can find C easily enough, since
\[f(e)=5=2\ln(e)+C=2+C\] making \(C=3\) and so your funciton is
\[f(x)=2\ln(x)+3\]

Answer 4

Then u plug in e right? But u get 2ln (e) +3 which is 5 but in teh answer key it says its 6

Answer 5

oh because i am an idiot

Answer 6

it says
\[f(\sqrt{e})=5\]

Answer 7

so we have
\[f(x)=2\ln(x)+C\] and we know that
\[f(\sqrt{e})+C=5\] so
\[2\ln(\sqrt{e})+C=5\]
\[1+C=5\] and so
\[C=4\]

Answer 8

therefore your function is
\[f(x)=2\ln(x)+4\] and then of course
\[f(e)=2\ln(e)+4=2+4=6\]
sorry about my original mistake

Answer 9

OH no problem! Thanks for finxing it! =)