MATH 2144 Midterm: MATH 2144 OK State PracticeExam3 sol
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Solution to practice problems for midterm 3: if the rectangle has dimension x and y, then its perimeter is 2x + 2y = 100. Thus, the area is a = xy = x(50 x) = 50x x2, where 0 x 50. Therefoe, we rst need to nd all critical points of a(x). Notice that a (x) = 50 2x = 0 only at x = 25. The area a(25) = 25(50 25) = 625, while. Clearly, the maximum area occurs at x = 25 and y = 50 x = 25, and the maximum area is a(25) = 625: let x > 0 and f (x) = x + 1 x . Notice that f (x) = 1 1 x2 = 0 implies 1 x2 = 1. We have two critical points, x = 1 and x = 1. However, since we only consider positive numbers x > 0, here we only take on critical point x = 1.
