Need help of max and min calculus, thank you

Question

In which interval is the function f(x) =  - x + 3 increasing?

Option:

1. (-∞, -1) only
2. (1, ∞) only
3.   (-∞, -1) U (1, ∞)
4. (-1, 1) only

Answer 1

Assuming that f(x) = (1/3)x³ - x + 3, then f'(x) = x² - 1. Setting f' = 0 gives local extrema at x = -1 and x = 1. Given it's a cubic function with a positive leading coefficient the function is increasing on (-∞, -1) U (1, ∞)...