y - A B x

Consider function f given by f(x) = 6 + 6*cos(x) for 0 ≤ x ≤ 4π.
Attached figure shows graph of y = f(x)
Graph of f touches X-axis at points A and B, as shown in accompanying figure. Shaded region is bounded by graph of y = f (x) and X-axis , between points A and B.

(a) Find X-coordinates of A and B.
(b) Show that area of shaded region is equal to 12π .