Please show all work to understand

1. Consider the function f (x) = sin x 2+cos x a) What is the domain of the function? b) Find the first derivative of the function. [Hint: use a trigonometric identity to simplify the first derivative]. What are the critical numbers? Limit your analysis to 0 S x 5 2n c) Use the first derivative to locate the intervals of increase or decrease as well as any local extrema. Show your work. (Indicate the (x,y) coordinates at which the local extrema occur and clearly specify whether it is a local max or local min). Limit your analysis to 0 Ex S 2n