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

##### 1 Answer

x=1

#### Explanation:

*By definition, the normal line must have a slope that is the opposite reciprocal of the slope of the tangent line at #x=1#.
Thus, to determine the slope of the normal line, we must first calculate the slope of the tangent line at x=1, which is just the derivative of #f# at #x=1# or #f'(1)#.*

Step 1: **Calculate #dy/dx#**

Step 2: **Find f'(1)**

Step 3: **Determine the equation of the normal line**

Knowing that

The equation for the vertical tangent line is