Chapter 4 - Applications of the Derivative - 4.2 Extreme Values - Exercises - Page 180: 5

6 and -3.

$ f'(x)$ exists for all x. Therefore, the only critical points are the solutions of $ f′(x)=0$ $ f'(x)=3x^{2}-9x-54=0$ Or $ x^{2}-3x-18=0$ $\implies x= 6$ or $ x=-3$ Thus, the critical points are the roots $ c=6$ and $ c=-3$.