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

[physicsdreams]

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!

 

[Dick]

No, you can't solve that algebraically. Proceed with a graphical solution.

 

[physicsdreams]

Thanks!