Find the local minima and maxima (or local extrema) of $f$. For each extremum, determine three things: its location (i.e., value of $x$), its value (i.e., value of $f(x)$), and whether it is a local maximum or a local minimum.

Find the global maximum and global minimum of the function $f(x)$ on the interval $\frac{5}{12} \le x \le 3$. Also indicate the location (the value of $x$) of the global maximum and global minimum.

Find the global maximum and global minimum of the function $f(x)$ on the interval $-4 \le x \le 2$. Also indicate the location (the value of $x$) of the global maximum and global minimum.