Suppose that y(x) is a solution of the autonomous equation dy/dx = f (y) and is bounded...

Suppose that y(x) is a solution of the autonomous equation dy/dx = f (y) and is bounded above and below by two consecutive critical points c₁ < c₂, as in subregion R2 of Figure 2.1.6(b). If f (y) 0 in the region, then limx:_ y(x) = c₂. Discuss why there cannot exist a number L < c₂ such that . As part of your discussion, consider what happens to