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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