(Solved): Consider the function f(x)=cos2(x) on [0,]. (a) Find the intervals on which f is increasing, decr ...

Consider the function $f(x)={\cos }^2(x)$ on $[0,?]$. (a) Find the intervals on which $f$ is increasing, decreasing, concave up, concave down (if they exist). If no such interval exists, write "NOWHERE" in the answer box. Show all work. Justifications must include derivatives and sign analysis. Give exact answers (e.g., write $?$ instead of 3.1416).