Answer:
All of the above
Step-by-step explanation:
dy/dt = y/3 (18 − y)
0 = y/3 (18 − y)
y = 0 or 18
d²y/dt² = y/3 (-dy/dt) + (1/3 dy/dt) (18 − y)
d²y/dt² = dy/dt (-y/3 + 6 − y/3)
d²y/dt² = dy/dt (6 − 2y/3)
d²y/dt² = y/3 (18 − y) (6 − 2y/3)
0 = y/3 (18 − y) (6 − 2y/3)
y = 0, 9, 18
y" = 0 at y = 9 and changes signs from + to -, so y' is a maximum at y = 9.
y' and y" = 0 at y = 0 and y = 18, so those are both asymptotes / limiting values.
