Bingo You were right, but what did you do to maximize each coordinate? Did you stick the intervals that x was between back into f(x)?
yes, i found f(-6) and f(15). if one of those is lower than the y-value of all critical poitns, then it is the absolute min, if one is higher than all the y-values of the critical points, it is the absolute max.
so always remember to check the endpoints for absolute max and mins