What is the equation of the line normal to # f(x)=lnx-x# at # x=2#?

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Answer 1 · 2016-06-09T12:41:01

#y = log_2(2)-2+2(x-2)#

taking #f(x)=Log_e(x)-x# the tangent space at each point is obtained
with

#m(x) = (df)/(dx) = 1/x-1#

Also the normal space direction is obtained with

#n(x) = -1/(m(x))#

In this case, at point #p_0 = {x_0,y_0} = (2,log_e(2)-2}# we have:

#n_0(2) = -1/((-1/2)) = 2#

Finally the normal straight at point #p_0# reads

#y = log_2(2)-2+2(x-2)#

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