(Solved): Answer to number 3 lesson 17 The correct answers are given for problems 1 and 2 . Remember to ...

Answer to number 3

lesson 17

The correct answers are given for problems 1 and 2 . Remember to check that the answer really s the maximum or minimum as required by the problem. This checking might take the form f evaluating the object function at critical points and end points of a closed interval of possible calues, or if the interval in not closed, the check will probably involve investigating the sign of the irst derivative. Warning: These problems can lead to headaches, chest pains, and baldness (from earing 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? (Answers: $$r=\sqrt[3]{\frac{V}{2?}},h=2\sqrt[3]{\frac{V}{2?}}.)$$ (3) A box with a square base and no top is to have a volume of $$32{\mathrm{ft}}^3$$. What dimensions use the least amount of material (in other words what dimensions give minimum outside 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 $$x$$-axis to the positive $$y$$-axis passing through the point $$(8,1)$$.