`f(x) = sin(x) cos(x) + 5` 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 function is continuous and differentiable on the given interval. It is increasing when f'(x)>0 and decreasing when f'(x)<0. Let's find f'(x).

f(x) = sin(x)*cos(x) + 5 = (1/2)*sin(2x) + 5.

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

It is zero at...

(The entire section contains 111 words.)

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