Find the points of inflection and discuss the concavity of the graph of the function.

so here's the function

f(x) = 2sinx + sin2x and in order to find the concavity i need to find the second derivative which is this.... f ''(x)= -2sinx - 4sin2x.... now how do i find the critical numbers to determine the concavity of the function? how to i set x equal to zero to find the critical numbers.... please help!!

Re: Find the points of inflection and discuss the concavity of the graph of the funct

Equating the second derivative to zero, we find:

$\displaystyle -2(\sin(x)+2\sin(2x))=0$

$\displaystyle \sin(x)+2\sin(2x)=0$

Now, use the double-angle identity for sine, then factor. What do you find?