(a) Answer The value of the derivative of the rabbit is zero in both cases. Explanation The number of rabbits is at its highest on day 40 and it is also clear from the graph the derivative at day 40 is zero. Again, it is clear from the graph that the number of rabbits approaches its lowest value as x increases also approaches zero. Therefore, the value of the derivative of the rabbit is zero in both cases. (b) To determine To find: the value of the derivative of the rabbit population in both condition. Answer The required graph is shown below. Explanation Given: The general equation is y = ( x − a ) ( x + b ) . As it is clear from the figure (b) the derivative reaches a maximum on day 20 and it is also clear from the graph (a) the population of rabbits is 1700 . Again, it is clear from the graph (b) the derivative a minimum on around day 63 . On that day, according to graph (a), the population of rabbits is about 1300 . Therefore, the rabbit size of the rabbit population are 1700 and 1300 respectively.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3.1, Problem 23E

(a)

To determine

To find: the value of the derivative of the rabbit population in both condition.

(a)

Expert Solution

Answer to Problem 23E

The value of the derivative of the rabbit is zero in both cases.

Explanation of Solution

The number of rabbits is at its highest on day 40 and it is also clear from the graph the derivative at day 40 is zero.

Again, it is clear from the graph that the number of rabbits approaches its lowest value as x increases also approaches zero.

Therefore, the value of the derivative of the rabbit is zero in both cases.

(b)

To determine

To find: the value of the derivative of the rabbit population in both condition.

(b)

Expert Solution

Answer to Problem 23E

The required graph is shown below.

Explanation of Solution

Given:

The general equation is y=(x−a)(x+b) .

As it is clear from the figure (b) the derivative reaches a maximum on day 20 and it is also clear from the graph (a) the population of rabbits is 1700 .

Again, it is clear from the graph (b) the derivative a minimum on around day 63 . On that day, according to graph (a), the population of rabbits is about 1300 .

Therefore, the rabbit size of the rabbit population are 1700 and 1300 respectively.

Chapter 3.1, Problem 22E

Chapter 3.1, Problem 24E

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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