Determine Where the Graph of the Function $f(x)=x^{3}-30 x$ Is Concave Upward and Where It Is Concave Downward

Determine where the graph of the function $f(x) =x^{3}-30 x$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

A) CU on $(-\sqrt{10}, \sqrt{10})$ , CD on $(-\infty,-\sqrt{10})$ and $(\sqrt{10}, \infty)$
IP $(-\sqrt{10}, 20 \sqrt{10})$ and $(\sqrt{10},-20 \sqrt{10})$
B) CU on $(0, \infty)$ , CD on $(-\infty, 0)$ ,
IP $(0,0)$
C) CU on $(-\sqrt{10}, \infty)$ , CD on $(-\infty,-\sqrt{10})$ ,
IP $(-\sqrt{10}, 20 \sqrt{10})$
D) CU on $(\sqrt{10}, \infty)$ , CD on $(-\infty, \sqrt{10})$ ,
IP $(\sqrt{10},-20 \sqrt{10})$

Correct Answer:

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