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 Author Comment/Response DC 03/17/13 11:11am When I type the code as follows: f[x_] := (x^4 - 2 x^3 + x^2 - 8)/(x^2 - 1) and find the second derivative, I get (2 - 12 x + 12 x^2)/(-1 + x^2) - ( 4 x (2 x - 6 x^2 + 4 x^3))/(-1 + x^2)^2 + ( 8 x^2 (-8 + x^2 - 2 x^3 + x^4))/(-1 + x^2)^3 - ( 2 (-8 + x^2 - 2 x^3 + x^4))/(-1 + x^2)^2. I then use the apart function and get the much simpler 2 - 8/(-1 + x)^3 + 4/(1 + x)^3 Then, when I set that = 0 and solve to find the critical points, I get {{x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 1]}, {x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 2]}, {x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 3]}, {x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 4]}, {x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 5]}, {x -> Root[-7 - 6 #1 - 15 #1^2 - 2 #1^3 - 3 #1^4 + #1^6 &, 6]}} I do not understand what I am looking at. I know where the critical values should be based on the graph, and I don't know how to find the answer within this output. What am I doing wrong? Thanks!! URL: ,

 Subject (listing for 'Critical Points of Second Derivative') Author Date Posted Critical Points of Second Derivative DC 03/17/13 11:11am Re: Critical Points of Second Derivative Bill Simpson 03/18/13 6:03pm
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