16 Nov 2021
Problem 32a
Page 307
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Textbook ExpertVerified Tutor
16 Nov 2021
Given information
A fish swimming at a speed relative to the water, the energy expenditure per unit time is proportional to . It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current , then the time required to swim a distance is and the total energy required to swim the distance is given by
where is the proportionality constant.
Step-by-step explanation
Step 1.
According to the question,
The total energy required to swim the distance is
Differentiate on both sides,
Note that is undefined if . So
When,