SOLUTION: Find the asymptotes, maxima and the minima of the following functions f(x)= 1/( x^3 + x^2 - x - 1)

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Question 861018: Find the asymptotes, maxima and the minima of the following functions
f(x)= 1/( x^3 + x^2 - x - 1)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

f(x)= 1/( x^3 + x^2 - x - 1)

Note:

x^3 + x^2 - x - 1  ,  x = 1 a root

Using Synthetic Division to find other roots

1	1	1	-1	-1

		1	2	1

	1	2	1	0

(x-1)(x^2 + 2x + 1) = (x-1)(x+1)(x+1)

Find the asymptotes, maxima and the minima of the following functions

f(x)= 1/( x^3 + x^2 - x - 1)

x-asymptotes are x = -1  and x = 1

y-asymptote is y = 0 for x = (−∞,-1) U (1,∞) 

maxima y = -0.8438 at x = 1/3   for -1%3C+x+%3C+1