Question

How do you find the local extrema for `f(x) = (x-3)^3` on (-∞, ∞)?

Answer 1

`f` has no local extrema.

Explanation:

`f'(x) = 3(x-3)^2` is never undefined and is `0` only at `0`, so the only critical number is `0`.

`f'(x)` is always positive for `x != 0`, so `f` is increasing on `(-oo,oo)`.