previous problem problem list next problem\n(-infinity,-2) u (2,infinity)\n(-2,2)\nat least one of the…

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = x^n$, then $y'=nx^{n - 1}$. For $f(x)=x^{3}-4.5x^{2}-12x - 3$, we have: $f'(x)=\frac{d}{dx}(x^{3})-\frac{d}{dx}(4.5x^{2})-\frac{d}{dx}(12x)-\frac{d}{dx}(3)$. Using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ and $\frac{d}{dx}(c)=0$ (where $c$ is a constant), we get $f'(x)=3x^{2}-9x - 12$.

Answer:

$3x^{2}-9x - 12$