Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.
f(x) = x³ - 27x + 9
a) Increasing on (-[infinity], 3) , decreasing on (3, [infinity]) , local extrema at x = 3
b) Increasing on (-[infinity], 3) , decreasing on (3, [infinity]) , no local extrema
c) Increasing on (-[infinity], [infinity]) , decreasing on (-[infinity], [infinity]) , no local extrema
d) Increasing on (-[infinity], [infinity]) , decreasing on (-[infinity], [infinity]) , local extrema at x = 3