# What is the slope of the line normal to the tangent line of #f(x) = 2x-4sqrt(x-1) # at # x= 2 #?

##### 1 Answer

Feb 22, 2017

The slope will be undefined.

#### Explanation:

Start by finding the y-coordinate of the point of tangency.

#f(2) = 2(2) - 4sqrt(2 - 1)#

#f(2) = 4 - 4#

#f(2) = 0#

Find the derivative of

#f'(x) = 2 - 4/(2sqrt(x - 1))#

#f'(x) = 2 - 2/sqrt(x - 1)#

Now find the slope of the tangent.

#f'(2) = 2 - 2/sqrt(2 - 1) = 2 - 2/1 = 0#

The normal line is perpendicular to the tangent line. The slope of

Hopefully this helps!