What is the equation of the normal line of $f(x)=1-lnx/x$ at $x=1$ ?

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Answer 1 · 2016-01-17T09:04:50

Normal Line
$y=x$

Given $f(x)=1-ln x/x$ and $x=1$
find $f(1)$

$f(1)=1-ln (1)/1$
$f(1)=1$
Use point $(1, 1)$

Find the slope of the Normal Line at $(1, 1)$
slope =-1/f' (1)#

$f' (x)=0+(-1)*(x*1/x-ln x*1)/x^2$
$f' (1)=(-1)*(1-ln 1)/1^2$
$f' (1)=-1$

slope m $= -1/-1=1$

Use point slope form

$y-y_1 = m (x-x_1)$

$y-1=1(x-1)$

$y=x$

What is the equation of the normal line of f(x)=1-lnx/xf(x)=1-lnx/x at x=1x=1?