At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing v³ E (v) v — C vk s v-c. For |‒‒ Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)
At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing v³ E (v) v — C vk s v-c. For |‒‒ Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:At what speed should a fish swim upstream so as to reach its destination with the
least expenditure of energy? The energy depends on the friction of the fish through
the water and on the duration of the trip. If the fish swims with velocity v, the energy
has been found experimentally to be proportional to (for constant k > 2) times the
duration of the trip. A distance of s miles against a current of speed c requires time
-c (distance divided by speed). The energy required is then proportional to
k = 3, minimizing energy is equivalent to minimizing
|-
v³
E(v) =
=
V C
vk s
v-c. For
Find the speed v with which the fish should swim in order to minimize its expenditure
E(v). (Your answer will depend on c, the speed of the current.)
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