# What are the points of inflection of #f(x)=8x + 3 - 2sinx # on # x in [0, 2pi]#?

The first step in finding the points of inflection is taking the second derivative of the function. So let's do that:

The points of inflection are points where the second derivative equals 0.

Just to make sure that the concavity actually DOES change at these points, let's use some test points to look at the concavity:

These points tell us that:

Final Answer

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The points of inflection of ( f(x) = 8x + 3 - 2\sin(x) ) on ( x ) in ([0, 2\pi]) are at ( x = \frac{\pi}{6} ) and ( x = \frac{5\pi}{6} ).

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