Points of inflection and concave

Question

Given the function 𝑓(𝑥) = 𝑥 − 2cos(𝑥) on [0, 2𝜋]

Part 1: Determine the open intervals on which the function is either concave

upward or concave downward.

Part 2: Determine the (𝑥, 𝑦) ordered pairs of the point(s) of inflection, if

there are any. If there are none, then state that.

Answer 1

The easiest way to answer this is to graph it!

Then use whatever algebra and calculus you need to support your answer.

Absolute minimum at x=0

There is a point of inflection somewhere near pi/2 a relative max near pi and a min at a little less than 2 pi.