THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x), where f is a differentiable function. 1. If f'(xo)

THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x),<br>where f is a differentiable function.<br>1. If f'(xo) < 0, then f is decreasing at xo and xo is asymptotically stable.<br>2. If f'(xo)<br>- 0, then f is increasing at xo and xo is unstable.<br>3. If f'(xo) = 0, no conclusion can be drawn.<br>

Extracted text: THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x), where f is a differentiable function. 1. If f'(xo) < 0,="" then="" f="" is="" decreasing="" at="" xo="" and="" xo="" is="" asymptotically="" stable.="" 2.="" if="" f'(xo)="" -="" 0,="" then="" f="" is="" increasing="" at="" xo="" and="" xo="" is="" unstable.="" 3.="" if="" f'(xo)="0," no="" conclusion="" can="" be="">

29. In Theorem 9.8, if f' (x o)<br>drawn about the equilibrium point xo of x' = ƒ(x). Ex-<br>plain this phenomenon by providing examples of equa-<br>tions x = f (x) where<br>0, no conclusion can be<br>(a) f' (xo) = 0 and xo is unstable, and<br>(b) f' (xo) = 0 and xo is asymptotically stable.<br>

Extracted text: 29. In Theorem 9.8, if f' (x o) drawn about the equilibrium point xo of x' = ƒ(x). Ex- plain this phenomenon by providing examples of equa- tions x = f (x) where 0, no conclusion can be (a) f' (xo) = 0 and xo is unstable, and (b) f' (xo) = 0 and xo is asymptotically stable.

Jun 03, 2022

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THEOREM 9.8 Suppose that xo is an equilibrium point for the differential equation x = f(x), where f is a differentiable function. 1. If f'(xo)

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