Calculus Homework #10 Due 5-11

1. A rectangle has a vertex on the x-axis between 0 and 9, a vertex at the point (9,0), a vertex on the line x=9, and a vertex on the curve y=\sqrt{x}. Find the dimensions of the rectangle having the maximum possible area.

2. To get the best view of the Statue of Liberty you should be at the position where \theta is a maximum. If the statue stands 92 meters high, including the pedestal, which is 46 meters high, how far from the base should you be?

Statue-of-Liberty-close

3. You run a small furniture business. You sign a deal with a customer to deliver some number of chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 300 ordered. What is the maximum amount of money your company can make on this order?

4. For which positive number x is x^{\frac{1}{x}} largest?