+4 Hey guys, any help with this is much appreciated! 
A) Find the critical number(s) of h(x)=sin(x)+cos(x)
B) Find the local minimum(s) and maximum(s) of h(x)
C) Does h(x) have any global minimum(s) or maximum(s)? If so, where?
+130511 h(x)=sin(x)+cos(x) find the derivative and set it to 0
h' (x) = cosx - sinx = 0 add sin x to both sides
cosx = sinx
The critical numbers occur at 45° + n360°
and at 225° + n360° where n is an integer
Taking the second derivative, we have
-sinx - cosx ...... and subbing 45° into this produces a negative.......so this indicates a max at 45° + n360°
Likewise subbing 225° into the second derivative produces a positive value......so this indicates a minimum at 225° + n360°
These points are both local and global maxes and mins since we are not restricted to any particular interval
Here's a graph: https://www.desmos.com/calculator/cnytd7bpfn
