Chapter 1.1, Problem 6E

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

How do the graphs of the functions f(x)=x2 and f(x)=x21 differ? We graphed them at the start of this section. What is the difference between their graphs? How are their graphs the same?

In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Bird Flight A bird is released from point A on an island. 5 mi from the nearest point Bon a straight shoreline. The bird flies to a point C on the shoreline and then flies along the shoreline to its nesting area D (see the figure). Suppose the bird requires 10 Kcal/mi of energy to fly over land md 14 kcal/mi to fly over water. a) Use the fact that energy used = energy per mile X miles flown to show that the total energy used by the bird is modeled by the function E(x)=14x2+25+10(12x) (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to whatpoint does it fly?