The derivative of a function $f$ is given by $f'(x) = x^2(x-3)$. For what value(s) of $x$ does the graph of $f$ have a relative minimum?

Core Concept

Correct. A relative minimum occurs where the derivative changes from negative to positive. The factor $x^2$ ensures $f'(x)$ is negative for all $x < 3$ (except $x=0$), and the factor $(x-3)$ makes $f'(x)$ positive for $x > 3$.