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X^3-2x-2cos(x) find local extrema

  1. Nov 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the local extrema of the function f(x)=(x^3-2x-2cos(x))

    2. Relevant equations

    derivatives, some algebra

    3. The attempt at a solution

    Well, the concept is simple.
    Solve for the first derivative and set it equal to zero:

    dy/dx=2sin(x)+3x^2-2=0 and

    Next, solve for x to determine the "critical points".

    My problem is in solving this seemingly simple equation algebraically.
    I can simplify it to:
    sin(x)=1-(3x^2)/2 (which doesn't help).

    I have a feeling that it's not possible to solve algebraically, (but that I can still graph it).
    Can anyone confirm my suspicion?

    Thanks in advance!
  2. jcsd
  3. Nov 15, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    No, you can't solve that algebraically. Proceed with a graphical solution.
  4. Nov 16, 2012 #3
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