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.

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.

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of (f(x)=3x^{3}-7) is (f^\prime(x) = 9x^{2}) using the power rule ((x^{n})^\prime=nx^{n - 1}).

Step2: Find the critical points

Set (f^\prime(x)=0), so (9x^{2}=0). Solving for (x), we get (x = 0).

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

As (x\to\infty), (y = f(x)=3x^{3}-7\to\infty) (since the leading term (3x^{3}) dominates). As (x\to-\infty), (y = f(x)=3x^{3}-7\to-\infty) (since the leading term (3x^{3}) dominates).

Answer:

B. There is no absolute minimum.