G Using calculus and the SDT (then FDT if necessary), find all global and local maximum and minimums given the function f(x) = x 3 + x 2 − x + 1 where x ∈ [−2, 1 2 ]. Clearly identify critical values and show the SDT then the FDT if the SDT didn’t provide an answer and then interpret the solution.

(Absolute minimum) and (Absolute maximum)

Step-by-step explanation:

The critical points are determined with the help of the First Derivative Test:

The critical points are:

and

The Second Derivative Test offers a criterion to decide whether critical point is an absolute maximum and whether is an absolute minimum:

(Absolute minimum)

(Absolute maximum)

The critical points are:

(Absolute minimum) and (Absolute maximum)

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !