find the absolute extremum, if any, for the following function.\n$f(x)=8x^{3}-1$\nselect the correct choice…
find the absolute extremum, if any, for the following function.\n$f(x)=8x^{3}-1$\nselect the correct choice below and, if necessary, fill in the answer boxes to complete your choice.\na. the absolute minimum is at $x=$\nthere 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)=8x^{3}-1) is (f^{\prime}(x)=24x^{2}).
Step2: Find critical points
Set (f^{\prime}(x) = 0), so (24x^{2}=0), which gives (x = 0).
Step3: Analyze the behavior of the function
As (x\to-\infty), (y = f(x)=8x^{3}-1\to-\infty). As (x\to+\infty), (y = f(x)=8x^{3}-1\to+\infty).
Answer:
B. There is no absolute maximum.