How do I find the extreme values for the function y=sinx+cosx on the interval 0<x<2(pi)

Answer 1

get the derivative to get the maximum/minimum:
y = sinx + cosx
y' = 0 = cosx - sinx
cos x = sin x

x=pi/4 *the value of x in which y is max
x=-(pi/4) *the value of x in which y is min

you can actually check this by graphing the equation,,

so there,, =)