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

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Answer 1 · 2016-09-17T02:51:27

#-4/47#

The slope of the line tangent to the curve #y=f(x)# at #x=2# is given by #f'(2)#.

First, find #f'(x)#.

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

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

Find #f'(2)# by substituting #x=2#.

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

#= 47/4#

The slope of the line normal to the tangent line, #m#, is given by

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

#= - 4/47#