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 $y \in (-6 \sqrt{3},8]$ .

C D B A

1 solution

Wee Xian Bin
Mar 4, 2016

A is not true because the local minima is within the given interval, hence the range should be denoted as the closed interval $y \in (-6 \sqrt{3},6 \sqrt{3} ]$ instead.

B is not true because the curve has 3 $x$ -intercepts and 1 $y$ -intercept ( If you chose this, gotcha! =D).

C is true because the area between the curve where $-2\leq x\leq1$ is equal to the area between the curve where $1\leq x\leq4$ .

D is not true, the range should be $[-6 \sqrt{3},8)$ instead.

Try to picture this cubic mentally

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