# What is the equation of the line that is normal to #f(x)= x/e^(2x-2) # at # x= 1 #?

##### 1 Answer

Apr 8, 2017

#### Explanation:

To find an equation of a line, we need two things:

- Point on the line:
#(x_1,y_1)=(1,f(1))=(1,1)# - Slope of the line:
#m=-1/(f'(1))=-1/(-1)=1#

(Note: Since the normal line is perpendicular to the tangent line, we take the negative reciprocal of the slope of the tangent line#f'(1)# .)

By Point-Slope Form

I hope that this was clear.

Here are more details:

By Quotient Rule,

So,