Ths physics of the situation requires that the wave function must fall smoothly to zero at both edges of the potential. This behavior is necessary because, when squared, this function gives the probability density for detecting the electron. The wave function must fall to zero near the edge of the potential and remain zero from there on because the probability to find the electron far from the potential must be zero. While the mathematics allows other results, the physics does not, so it must be excluded from possibility.
Experiment with clicking at nearby energies to try to improve the wave function. If you want to compare one wave function with another, click the Keep button to save it.
At some time, you should end up with wave functions on opposite sides of what is needed. One will go to positive infinity, and the other to negative infinity as shown in the figure.