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#