Sketch graphs of two functions, as in Figure 3.7. (No equations are needed.) For each function, which we'll refer to as f (X), sketch the vector field of X = f (X). Mark the equilibrium points and indicate their stability. the graph below is the figure 3.7

Exercise 3.2.7 Sketch graphs of two functions, as in Figure 3.7. (No equations are needed.) For each function, which we'll refer to as f(X), sketch the vector field of X' = f(X). Mark the equilibrium points and indicate their stability. __ . \\")' . . ' .._._ .. l'"""' _._'__, .. _.._.... ... . 'D"" .... X' = f(X) Figure 3.7: Vector eld plot for logistic vector eld. The black curve shows X' at each point X in state space. The points in X at which the curve intersects the horizontal axis (X' = 0) are equilibrium points of the vector field. Here they are at X = 0 and X = k