find the absolute extremum, if any, for the following function.\nf(x)=3x^{3}-7\nselect the correct choice…

find the absolute extremum, if any, for the following function.\nf(x)=3x^{3}-7\nselect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute minimum is at x=\n b. there is no absolute minimum.\nselect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum is at x=\nb. there is no absolute maximum.

find the absolute extremum, if any, for the following function.\nf(x)=3x^{3}-7\nselect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute minimum is at x=\n b. there is no absolute minimum.\nselect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute maximum is at x=\nb. there is no absolute maximum.

Answer

Explanation:

Step1: Find the derivative

The derivative of (f(x)=3x^{3}-7) is (f^\prime(x)=9x^{2}).

Step2: Find critical points

Set (f^\prime(x) = 0), so (9x^{2}=0), which gives (x = 0).

Step3: Analyze the behavior of the function as (x\to\pm\infty)

As (x\to\infty), (f(x)=3x^{3}-7\to\infty). As (x\to-\infty), (f(x)=3x^{3}-7\to-\infty).

Answer:

B. There is no absolute minimum. B. There is no absolute maximum.