Expert: Paul Klarreich - 4/9/2008

Question
what are the critical point for the function 2+x-2xsquared-x to the power of 3?

Answer
Questioner:   Jules
Category:  Advanced Math
Private:  No
 
Subject:  Not sure
Question:  what are the critical point for the function 2+x-2xsquared-x to the power of 3?
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Hi, Jules,

Is this a calculus question? It looks like it, because 'critical point' is a calculus concept.  So you should send future questions to me under the Calculus heading. [Unless it's filled up, of course.  Then you can send it to me here -- no problem.]

Your problem : (This is how to write it -- read some other answers to get an idea of how to write math on this site.)

f(x) =  2 + x - 2x^2 - x^3

Critical points are:

1) Stationary points: values where f'(x) = 0.  
2) Singular points: values where f'(x) is undefined.  
3) Endpoints.

f'(x) = 1 - 4x - 3x^2

Set that equal to zero.

1 - 4x - 3x^2 = 0

-1 + 4x + 3x^2 = 0
3x^2 + 4x - 1 = 0

Does not factor.  Use the Q.F.:

   - 4 +- sqrt(16 + 12)
x = ----------------------
              6  

   - 4 +- sqrt(28)
x = ----------------
          6  

   - 4 +- 2 sqrt(7)
x = ----------------
          6  

   - 2 +- sqrt(7)
x = ----------------
          3  

Those are your stationary points.  You don't have any of the other kind.