Which of the equilibria, if any, are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. There is one stable equilibrium when and there are no stable equilibria for other values of h. (Type your answer in inequality notation.) OB. There are two stable equilibria when and there are no stable equilibria for other values of h. (Type your answer in inequality notation.) OC. All of the equilibria are stable for all values of h. O D. The equation does not have equilibria for any value of h.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.8: Interpreting Graphs Of Functions
Problem 4CYU
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FInd part 3

Treat h as a constant. For what values of h (if any) does the following equation have equilibria? Use a graphical argument to show which of the equilibria (if any) are stable.
dy
dx
=y5-2y-h
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The equation has equilibria for
(Type an inequality.)
B. The equation has equilibria for all values of h.
C. The equation does not have equilibria for any value of h.
Separate the equation into two parts and graph each part. Indicate the direction in which y(x) moves. Choose the correct graph below.
A.
Ady/dx
3-
Y3
O B.
Ady/dx
3-
O C.
-3
Ady/dx
3-
O A. There is one stable equilibrium when, and there are no stable equilibria for other values of h.
(Type your answer in inequality notation.)
Y3
Which of the equilibria, if any, are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OB. There are two stable equilibria when and there are no stable equilibria for other values of h.
(Type your answer in inequality notation.)
OC. All of the equilibria are stable for all values of h.
O D. The equation does not have equilibria for any value of h.
O D.
Ady/dx
3-
AV
Y3
Q
Transcribed Image Text:Treat h as a constant. For what values of h (if any) does the following equation have equilibria? Use a graphical argument to show which of the equilibria (if any) are stable. dy dx =y5-2y-h Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The equation has equilibria for (Type an inequality.) B. The equation has equilibria for all values of h. C. The equation does not have equilibria for any value of h. Separate the equation into two parts and graph each part. Indicate the direction in which y(x) moves. Choose the correct graph below. A. Ady/dx 3- Y3 O B. Ady/dx 3- O C. -3 Ady/dx 3- O A. There is one stable equilibrium when, and there are no stable equilibria for other values of h. (Type your answer in inequality notation.) Y3 Which of the equilibria, if any, are stable? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OB. There are two stable equilibria when and there are no stable equilibria for other values of h. (Type your answer in inequality notation.) OC. All of the equilibria are stable for all values of h. O D. The equation does not have equilibria for any value of h. O D. Ady/dx 3- AV Y3 Q
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