# Try to picture this cubic mentally

Calculus Level 2

Consider the curve of the following graph: $y=x^3-3 x^2-6 x+8$ Which statement is true?

A: The corresponding range of the function $$f: x \rightarrow x^3-3 x^2-6 x+8$$ for the semi-closed interval $$x \in [-2,4)$$ is $$y \in (-6 \sqrt{3},6 \sqrt{3} ]$$ .

B: The curve has 3 axial intercepts in total.

C: The integral $$\int_{-2}^{4} x^3-3 x^2-6 x+8 dx$$ is 0.

D: The corresponding range of the function $$f: x \rightarrow x^3-3 x^2-6 x+8$$ for the semi-closed interval $$x \in (0,4]$$ is $$y \in (-6 \sqrt{3},8]$$ .

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