MARINE BIOLOGY When a fish swims upstream at a speed v against a constant current vw, the...

MARINE BIOLOGY When a fish swims upstream at a speed v against a constant current vw, the energy it expends in traveling to a point upstream is given by a function of the form

S

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 number. Does it correspond to a relative maximum or a relative minimum?

b. Note that the critical number in part (a) depends on k. Let F (k) be the critical number. Sketch the graph of F(k).What can be said about F(k)if k is very large?