For the function f (x) = tan(x) 4x on the interval (/2, /2), determine the critical points, on which intervals f (x) is increasing, on which intervals f (x) is decreasing, on which intervals f (x) is concave up, and on which intervals f(x) is concave down. Find the local extrema using the second derivative test. Use this information to sketch the graph.

(This problem has many steps; explain the significance of each step and how they fit together.)