Question

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(-infinity,-2) u (2,infinity)
(-2,2)
at least one of the answers above is not correct.
f(x)=x^{3}-4.5x^{2}-12x - 3
a) find f(x).
b) identify the graph that displays f in blue and f in red.

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:

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