Let $g(x) = x^4 - 4x^3$. On what open interval(s) is the graph of $g$ concave down?

Core Concept

Correct. The second derivative is $g''(x) = 12x^2 - 24x = 12x(x - 2)$. Setting $g''(x) < 0$ yields $0 < x < 2$, which corresponds to the graph being concave down.