f(x)=sinx+cosx
(1)
f'(x)=cosx-sinx=0
cosx=sinx
tanx=1
x0=π/4
or
x0=5π/4
(2)
x0为驻点,f(x0)为极值[x0=π/4取极大值,x0=5π/4取极小值].