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When a fish nothing river up at a speed v. against a stream vw , the energy that expends to travel to a river point above is given by a function of the form: Cyk E(v) = v – Vw where C>0 and k >2 is a number that depends on the species of fish involved. a) Show that E(v) has exactly one critical point and explain whether this point is a relative minimum or maximum. b) The critical number in part a) depends on k. Let F (k) be the function of the critical number. Graph F(k). What can be said about F(k) if k is very large

When a fish nothing river up at a speed v. against a stream vw , the energy that expends to travel to a river point above is given by a function of the form: Cyk E(v) = v – Vw where C>0 and k >2 is a number that depends on the species of fish involved. a) Show that E(v) has exactly one critical point and explain whether this point is a relative minimum or maximum. b) The critical number in part a) depends on k. Let F (k) be the function of the critical number. Graph F(k). What can be said about F(k) if k is very large

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When a fish nothing river up at a speed v. against a stream vw , the energy that expends to travel to a river point above is given by a function of the form: Cyk E(v) = v - Vw where C> 0 and k >2 is a number that depends on the species of fish involved. a) Show that E(v) has exactly one critical point and explain whether this point is a relative minimum maximum. b) The critical number in part a) depends on k. Let F (k) be the function of the critical number. Graph F(k). What can be said about F(k) if k is very large
Transcribed Image Text:When a fish nothing river up at a speed v. against a stream vw , the energy that expends to travel to a river point above is given by a function of the form: Cyk E(v) = v - Vw where C> 0 and k >2 is a number that depends on the species of fish involved. a) Show that E(v) has exactly one critical point and explain whether this point is a relative minimum maximum. b) The critical number in part a) depends on k. Let F (k) be the function of the critical number. Graph F(k). What can be said about F(k) if k is very large
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