# What is the equation of the line normal to # f(x)=3(x-1)^2-6x+4# at # x=-2#?

##### 1 Answer

Jan 11, 2016

#### Explanation:

Find the point the normal line will intercept.

#f(-2)=3(-2-1)^2-6(-2)+4=43#

The normal line will intercept the point

To find the slope of the normal line, know that the normal line is perpendicular to the tangent line. The slope of the tangent line can be found through calculating

Find

#f'(x)=2*3(x-1)*d/dx[x-1]-6#

#=6(x-1)-6#

#=6x-12#

The slope of the tangent line is:

#f'(-2)=6(-2)-12=-24#

Thus, the slope of the *normal* line will be

Relate the slope of

#y-43=1/24(x+2)#