I am trying to find the intervals on which f is increasing or decreasing, local min and max, and concavity and inflextion points for $f(x)=\sin x+\cos x$ on the interval $[0,\pi]$.
I know at $\pi/4$ the derivative will equal zero. So that gives me my critical numbers, positive and negative $\pi/4$ so now I need to find the intervals which is not making any sense to me, I thought they could only change at critical numbers but $\pi$ and $2\pi$ are different values. I am getting a positive for $2\pi$ and a negtive for $\pi$. How can this happen if the only critical number is $\pi/4$?