17.4. Lesson 17 Problem Set The correct answers are given for problems 1 and 2. Remember to check that the answer really is the maximum or minimum as required by the problem. This checking might take the form of evaluating the object function at critical points and end points of a closed interval of possible values, or if the interval in not closed, the check will probably involve investigating the sign of the first derivative. Warning: These problems can lead to headaches, chest pains, and baldness (from tearing out your hair). (1) Using the methods of this lesson, find two positive numbers with sum 100 and product as large as possible. (Answer: both numbers are 50.) (2) A tin can (right circular cylinder) with top and bottom is to have volume V. What dimensions (the radius of the bottom and the height) give the minimum total surface area? VI Answers: r -1/7 - 2T 2n square base and no top is to have n volume of 32 fts. What dinensions use the least amount of material (in other words what dimensions give minimum outside (3) A box with surface area)? (4) Find the largest area possible for a rectangle inscribed in a circle of radius r. (5) (Bonus question): Find the shortest (straight line) distance from the positive s-axis to the positive y-axis passing through the point (8. I).