determine on which open intervals the function f(x) = x^3-3x+7 is increasing or decreasing?

f'(x) = 3x^2 - 3

Where is f(x) increasing?
f'(x) > 0
3x^2 - 3 > 0
3x^2 > 3
x^2 > 3/3
x^2 > 1
x > sqrt(1) or x < -sqrt(1)
x > 1 or x < -1

Where is f(x) decreasing?
f'(x) < 0
3x^2 - 3 < 0
3x^2 < 3
x^2 < 3/3
x^2 < 1
-sqrt(1) < x < sqrt(1)
-1 < x < 1