`f(x) = 2sin(x) + sin(2x), [0, 2pi]` Find the points of inflection and discuss the concavity of the graph of the function.

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Given f(x)=2sin(x)+sin(2x) on the interval [0,2pi], find the points of inflection and discuss the concavity:

Find the second derivative:

f'(x)=2cos(x)+2cos(2x)

f''(x)=-2sin(x)-4sin(2x)

Inflection points occur when the second derivative is zero (and changes sign.)

-2sinx-4sin(2x)=0

-8sin(x)cos(x)-2sin(x)=0    Using the...

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