1. ## Analyze trig function

I'd like to verify if this is right..

y=2cos(x)+sin(2x)
y ' = 2(-sin(x)+cos(2x))
y '' = -2(cos(x)+2sin(2x))

So I can use the y' to get the maximum, since pi/6 will give zero for the inside there. How can I analyze the y''? Change the 2sin(2x) to 4sinxcosx? I tried that and so then you can take out the cosx, which would mean that pi/2 would be one of the zeroes. What about the inside? (1+4sinx)?

2. Originally Posted by theowne
I'd like to verify if this is right..

y=2cos(x)+sin(2x)
y ' = 2(-sin(x)+cos(2x))
y '' = -2(cos(x)+2sin(2x))

So I can use the y' to get the maximum, since pi/6 will give zero for the inside there. How can I analyze the y''? Change the 2sin(2x) to 4sinxcosx? I tried that and so then you can take out the cosx, which would mean that pi/2 would be one of the zeroes. What about the inside? (1+4sinx)?
looks good so far

$\displaystyle 1+4\sin(x)=0 \iff \sin(x)=-\frac{1}{4} \iff x=\sin^{-1}\left(\frac{-1}{4} \right)$

3. So if the domain specifies between 0 and pi, do you discard that answer?