What is the equation of the line that is normal to #f(x)= x(x-4) # at # x= 5 #?

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Answer 1 · 2018-03-07T13:50:14

#f(x) = x^2-4x

#f(5) = 25-20#

#f(5) = 5#

#f'(x) = 2x-4#

#f'(5) = 2(5) -4#

#f'(5) = 6#

If #6# is the slope of the tangent, then #1/6# is the slope of the normal

#y-5 = 1/6(x-5)#

#y=x/6-5/6+30/6#

#y=x/6+25/6#

#6y=x+25#