Figure 3.14 b demonstrates the difference between the linearized approximation and the analytical solution of the fluid level as a function of time for a large step input. From the figure, the linearized curve indicates a negative level after approximately three hours. This certainly defies the physical properties of a tank.

The linearized approximations provide us with just that, approximations. Due to the properties of the Taylor series expansions, as you move farther from the base point from which the expansion is centered, the approximation becomes less accurate.  At this point, the linearized model is no longer able to predict the behavior.