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The minimum value of the function is at . This is a minimum value because is greater than . The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is . occurs at. Find the value of equal to . Substitute in the values of and . Remove the extra parentheses from the expression .
So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the boundary, and take the largest (or smallest) one.