Question 861018
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
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 = (&#8722;&#8734;,-1) U (1,&#8734;) 
maxima y = -0.8438 at x = 1/3   for {{{-1< x < 1}}}
{{{drawing(300,300,   -6, 6, -6, 6, grid(1), blue(line(1,6,1,-6)) ,blue(line(-1,6,-1,-6)) ,

circle(1/3, -.8438,0.2),
graph( 300, 300, -6, 6, -6, 6,0,1/( x^3 + x^2 - x - 1) ) )}}}