Let f(θ)=sin⁡(θ)+cos⁡(θ)\displaystyle {f{{\left(\theta\right)}}}={\sin{{\left(\theta\right)}}}+{\cos{{\left(\theta\right)}}}.

Calculate the derivative
f′(θ)=\displaystyle {f}'{\left(\theta\right)}=  

Calculate the second derivative
f′′(θ)=\displaystyle {f}{''}{\left(\theta\right)}=  

Note intervals are entered in the format (-00,5)U(7,oo) (these are two infinite intervals). Enter "DNE" if the interval is empty.

List the first interval after 0 on which f\displaystyle {f} is increasing?
Increasing:  

List the first interval after 0 on which f\displaystyle {f} is decreasing?
Decreasing:  

List the first interval after 0 on which f\displaystyle {f} is concave downward?
Concave Down:  

List the first interval after 0 on which f\displaystyle {f} is concave upward?
Concave Up:  

Sketch the graph and submit with your work.

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