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

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Answer 1 · 2016-11-11T18:38:07

$f$ has no local extrema.

$f'(x) = 3(x-3)^2$ 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 $(-oo,oo)$ .

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