Consider the function $f(x)=x^3-3x^2+4$. On which intervals is $f$ increasing?

Step-by-step solution

1. Differentiate the function: $f^{\prime }(x)=3x^2-6x$.
2. Factor the derivative: $f^{\prime }(x)=3x(x-2)$.
3. Set $f^{\prime }(x)>0$ to find where the function is increasing.
4. Solve the inequality $3x(x-2)>0$ which gives $x<0$ or $x>2$.
5. Hence the increasing intervals are $(-\infty ,0)$ and $(2,\infty )$.

Concept tested: Increasing / decreasing intervals

Published 6 September 2026 · How this solution was prepared and checked