A theorem states that if f is continuous on an interval I that contains one local extremum at c and if a local minimum occurs at Verify that the following function satisfies the conditions of this theorem on its domain. Then, find the location and value of the absolute extremum guaranteed by the theorem. f(x) = -xe -x The function f(x) = -xe -x has an absolute extremum of (Type exact answers.) at x=

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…