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Consider the function on the interval (0,2π). f(x)=x+2sinx (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing (32π​) decreasing (0,35π​),(3π​,2π)× (b) Apply the First Derivative Test to identify the relative extrema. relative maximum (x,y)=() relative minimum (x,y)=(3π​,3π​−3​×)
Consider the function on the interval (0,2π). f(x)=sin(x)cos(x)+2 (a) Find the open interval(s) on which the function is increasing or decreasing. increasing (0,4π​),(43π​,45π​),(47π​,2π) decreasing (4π​,43π​),(45π​,47π​) (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x,y)=(4π​,217​) (smallest x-value) relative minima relative minima (x,y)=(x)=( )
Consider the function on the interval (0,2π). f(x)=2x​+sin(x) (a) Find the open intervals on which the function is increasing or de increasing (0,32π​)∪(34π​,2π) decreasing (32π​,34π​) (b) Apply the First Derivative Test to identify the relative extrema. relative maximum (x,y)=(x) relative minimum (x,y)=( (c) Use a graphing utility to confirm your results.