Mathematics

Problem

Let

p(x)=\sin x+\cos x

on the interval

0\le x\le 2\pi

. On which intervals is

p

increasing? a)

(0,\tfrac{\pi}{4})

and

(\tfrac{5\pi}{4},2\pi)

(\tfrac{\pi}{4},\tfrac{5\pi}{4})

only c)

(0,\tfrac{\pi}{2})

and

(\pi,\tfrac{3\pi}{2})

(0,\tfrac{\pi}{4})

only