$($a$)(2$ points$)$ Consider the above plot of the growth rate $f(x)$ versus the population $x$ for the equation $\frac{dx}{dt}=f(x)$ with $x0.$ Draw the phase line. Mark all equilibrium populations, and draw in the arrows.

$($b$)(3$ points$)$ Recall the logistic equation $x^{\text{'}}=x-x^2.$ Find the two equilibria for this equation, and use the first derivative test to determine their stability. Hint: the sign of the slope, or first derivative, is related to the stability of the equilibrium.

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