Find the Extrema of the Function on the Given Interval $\sin x + \cos x , 0 \leq x \leq 2 \pi$

Multiple Choice

Find the extrema of the function on the given interval, and say where they occur.
- $\sin x + \cos x , 0 \leq x \leq 2 \pi$

A) local maxima: 1 at $x = 0$ and $- \sqrt { 2 }$ at $x = \frac { 5 \pi } { 4 }$ ;
local minima: 1 at $x = 2 \pi$ and $\sqrt { 2 }$ at $x = \frac { \pi } { 4 }$

B) local maxima: 1 at $x = 2 \pi$ and $\sqrt { 2 }$ at $x = \frac { \pi } { 4 }$ ;
local minima: 1 at $x = 0$ and $- \sqrt { 2 }$ at $x = \frac { 5 \pi } { 4 }$

C) local maxima: 1 at $x = 2 \pi$ and $\sqrt { 2 }$ at $x = \frac { \pi } { 4 }$ ;
local minima: 1 at $x = 0$ and $- \sqrt { 2 }$ at $x = \frac { 7 \pi } { 4 }$

D) local maxima: 1 at $x = 0$ and $- \sqrt { 2 }$ at $x = \frac { 7 \pi } { 4 }$ ;
local minima: 1 at $x = 2 \pi$ and $\sqrt { 2 }$ at $x = \frac { \pi } { 4 }$