The function $f(x)=x^3-3 x^2+6$ is an increasing function for:

• A

  $0 \lt x \lt 2$
• B

  $x \lt 2$
• Correct answer
  C

  $x \gt 2$ or $x \lt 0$
• D

  all $x$

Hence, the correct answer is option: 'C'.