Find the critical points and equilibrium solutions of the given autonomous differential equations dx/dt = f(x). Analyze the sign of the first derivative to determine the shape of solution curves, construct the corresponding phase diagram for each differential equation. Use second derivative test to determine inflection points and intervals where solutions curves concave up and concave down. Sketch typical solution curves; assess the stability of each critical point.
A. dx/dt = 3x - x²
B. dx/dt = (x - 2)²
C. dx/dt = x (x² - 4)
D. dx/dt = x³ (x² - 4)