# What is the slope of the line normal to the tangent line of #f(x) = 1/x+x^3 # at # x= 2 #?

##### 1 Answer

Sep 17, 2016

#### Explanation:

The slope of the line *tangent* to the curve

First, find

#f'(x) = frac{d}{dx}(1/x + x^3)#

#= -1/x^2 +3x^2#

Find

#f'(2) = -1/2^2 + 3(2)^2#

#= 47/4#

The slope of the line normal to the tangent line,

#m = -1/(f'(2))#

#= - 4/47#