`f(x) = x/2 + cos(x)` Consider the function on the interval (0, 2pi). Find the open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.

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This functions is infinitely differentiable. To find its extrema we have to solve the equation f'(x)=0:

f'(x)=1/2 - sin(x).  This is zero at...

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