Consider the function on the interval (0, 2𝜋). f(x) = sin x + cos x (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

Answer 1

f'(x)=cos(x)-sin(x)

f'(x)>0,,,,,0<x<π/4 and 5π/4<x<2π,,,,means f(x) increasing

f'(x)<0,,,,π/4<x<5π/4,,,,,means f(x) decreasing