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)

its a straight line parallel to the time axis