Graph analysis with trig involved

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The discussion revolves around analyzing the function y = sin(2x) - 2sin(x) through its derivatives. The user has successfully found the roots and the first and second derivatives but is uncertain about determining the roots of these derivatives to identify minima, maxima, and inflection points. There is confusion regarding whether the inflection point is zero and its implications for concavity. The original function is confirmed to be differentiable and continuous, and there is a need to clarify how to find the domain and range. The suggestion to use the double angle formula for the first derivative is noted as a potential step forward.
airportman92
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Homework Statement


given: y=sin2x-2sinx


Homework Equations





The Attempt at a Solution



i already found the roots of the equation, i also found the first and second derivatives which are 2cosx2-2cosx and -4sin2x+2sinx. however, i do not know how to find the roots for these equations in order to do mins and maxes and inflection pt. is it true that the inflection piont is zero, because that's how someone said to do it, but would that mean no concavity at all? and the original is differentiable and continuous correct? also, how wouuld i find the domain and range of this?
 
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For the first derivative, use the double angle formula

cos2x=2cos2x-1 = 1-2sin2x

Solve for x and sub that into the expression for y''.
 

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