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(Strogatz 2.4.1-6) In this question, we will consider the ODE

`x^(?)(t)=f(x(t)),`

for various choices of right-hand side

`f`

. Find the fixed points. Classify the linear stability of the fixed points. If linear stability analysis fails, use a graphical argument to determine the stability. Do the above tasks for the following choices of

`f`

. (a)

`f(x)=x(1-x)`

(b)

`f(x)=x(1-x)(2-x)`

(c)

`f(x)=tanx`

(d)

`f(x)=x^(2)(6-x)`

(e)

`f(x)=1-e^(x^(2))`

(f)

`f(x)=1-e^(-x^(2))`

(g)

`f(x)=logx`