determine whether Rolle's theorem can be applied, if it can be applied, determine all of the values of c.
f(x)=cos2x [-π,π]

Question

determine whether Rolle's theorem can be applied, if it can be applied, determine all of the values of c.
f(x)=cos2x [-π,π]

anonymous · Answer

if someone could help me out by solving this problem step by step that'd be great, thanks!

anonymous · Answer

it can certainly be applied because cosine is a continuous and differentiable function

anonymous · Answer

so how exactly what i go with this function, would I find the derivative of cos2x and plug in π and -π?

anonymous · Answer

into the derivative equation

anonymous · Answer

oh it is $\cos(2x)$ sorry
no matter it is still true that $\cos(2\pi)=\cos(-2\pi)$

anonymous · Answer

since the function is equal at the endpoints, rolle's theorem says that the derivative is equal to zero somewhere between $-\pi$ and $\pi$

anonymous · Answer

the derivative is $-2\sin(2x)$ set it equal to zero and solve for $x$

anonymous · Answer

so then the interval is only there so that I can make sure the equation applies to rolle's theorem? and I just have to solve the derivative for x then?

anonymous · Answer

your last job is to solve 
$$-2\sin(2x)=0$$ for $x$

anonymous · Answer

don't think too hard for this one, since $\sin(0)=0$ you get $2x=0,x=0$

anonymous · Answer

oh ok, I just didn't know what the intervals where there for, thanks for the help I appreciate it.

anonymous · Answer

np
you see that 0 is right there in the middle of your interval

anonymous · Answer

yeah I definitely understand that since it's in the middle of π and -π