What is the equation of the normal line of #f(x)= x^2 − 5x + 1# at #x = 5#?

1 Answer
mason m
Nov 16, 2015

#y=-1/5x+2#

Explanation:

Find the slope of the tangent line at the point #(5,1)# using the derivative. Then, write the equation of the line with a perpendicular slope at the point #(5,1)#.

Remember that #d/(dx)[ax^n]=nax^(n-1)#, where #a# is a constant.
#f'(x)=2x-5#
#f'(5)=5#

Therefore, if the slope of the tangent line at #x=5# is #5#, the perpendicular slope of the normal line is #-1/5#.

Write in point-slope form: #y-1=-1/5(x-5)#

In slope-intercept form: #y=-1/5x+2#

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