Explanation Given information: The Ricker curve, used to model the fish populations, is given by the function y = a x e − b x Where x is the number of adults, y is the number of offspring, and a and b are constants. Fact used: If f ' changes from negative to positive at p, then f has a local minimum at p. f ' changes from positive to negative at p, then f has a local maximum at p. Calculation: y = a x e − b x (Given) Differentiating with respect to ‘x’, we get y ' = a [ e − b x + x e − b x ( − b ) ] = a e − b x − a b x e − b x To find the critical points of y, set y ' = 0 ⇒ a e − b To determine (b) To explain: The global maximum in terms of population.

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.3, Problem 55P

To determine

(a)

To find and classify:

All critical points of the Ricker curve.

To determine

(b)

To explain:

The global maximum in terms of population.

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Chapter 4.3, Problem 54P

Chapter 4.3, Problem 56P

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APPLIED CALCULUS (WILEY PLUS)

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(a) To find and classify: All critical points of the Ricker curve.