Mathematica 9 is now available
Student Support Forum
-----
Student Support Forum: 'Critical Points of Second Derivative' topicStudent Support Forum > General > "Critical Points of Second Derivative"

Next Comment >Help | Reply To Topic
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
Next Comment >Help | Reply To Topic