Science:Math Exam Resources/Courses/MATH105/April 2016/Question 01 (d)/Solution 1

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Suppose that and that the domain of is (i.e., the set of points satisfying and ).

Since and , clearly has an absolute minimum of at and an absolute maximum of at .

However, neither nor is a critical point of because (recall that a critical point of is a point at which ).

Therefore, the statement is true.