Chapter 2, Problem 31P

Bird Flight A bird is released from point A on an island, 5 mi from the nearest point B on 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 and 14 kcal/mi to fly over water.

1. (a) Use the fact that

$\text{energy}\text{used}\text{=}\text{energy}\text{per}\text{mile}\text{×}\text{miles}\text{flown}$

to show that the total energy used by the bird is modeled by the function

$E(x)=14\sqrt{x^2+25}+10(12-x)$

1. (b) If the bird instinctively chooses a path that minimizes its energy expenditure, to what point does it fly?