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

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SUMMARY

The discussion focuses on finding local extrema for the function f(x) = x^3 - 2x - 2cos(x). The first derivative, dy/dx = 3x^2 + 2sin(x) - 2, is set to zero to identify critical points. Participants confirm that the equation cannot be solved algebraically and recommend using graphical methods to analyze the function's behavior. The conclusion emphasizes the necessity of graphical solutions for this type of equation.

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Homework Statement

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

Homework Equations



derivatives, some algebra

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!
 
Physics news on Phys.org
No, you can't solve that algebraically. Proceed with a graphical solution.
 
Thanks!
 

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