Answer: (D) asymptotically stable and semi-stable
Step-by-step explanation:
Given that:
dy/dx=(−(y−4)2)(y+9)
The critical points are y=4 and y=−9
We have to check the sign of dy/dx in the intervals (-inf,-9), (-9,4), (4, infinity)
In (-inf, -9), dy/dx , let's take y = -10, so we have
(-(-10-4)^2(-10+9) > 0
In (-9,4), let's take y = 0
dy/dx = (-(0-4)^2)(0+9) < 0
In (4, inf), let's take y = 10
So we have (-(10-4^)2(10+9) < 0
So at y = -9, sign change for dy/dx from positive to negative. SO it is asymptotically stable
And at y = 4, sign is negative on both sides. So 4 is semi stable
