Answer:
f(x) = x3 - 3x + 1
f'(x) = 3x2 - 3 = 3(x2 - 1) = 3(x+1)(x-1)
Find the critical numbers: set f'(x) = 0
3(x+1)(x-1) = 0 x = 1, -1
Check the sign of f'(x) on either side of each critical number. If f'(x) is positive on an interval, then f is increasing on the interval. If f'(x) is negative on an interval, then f is decreasing on the interval.
+ l - l + sign f'(x)
-------------------------------------
-1 1
f is increasing on (-∞, -1) υ (1, ∞)
f is decreasing on (-1, 1)