using Rolles theorem to see if it can be applied to f. If so, find all numbers c such that f`(c)=0 f(x)=sin(x)+cos(x) interval [0,2pi]

Answer 1

since the period of sin and cos is 2pi, the function clearly satisfies Rolle's Theorem.

So, we want to find c (possibly more than one value) where

f'(c) = 0
f'(x) = cosx - sinx
so, f'(c) = 0 if cosx = sinx
That is when x = pi/4 or 5pi/4

See the graph at

http://www.wolframalpha.com/input/?i=sinx%2Bcosx