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

##### 1 Answer

It is

#### Explanation:

We can first find the tangent to that curve in the point

The slope of the tangent is given by the derivative

This is the slope of the tangent line. The normal line is orthogonal to this line. The slope of the orthogonal line is

Then the normal has slope

The equation of the line is

I substitute this in the equation of the normal line

Then the equation of the normal is