The function is odd, with a horizontal tangent line at the origin and tails approaching zero from below on the negative side and above on the positive side. It decreases to its negative minimum at , rises through the stationary inflection point at zero to its positive maximum at , then decreases toward zero.
Figure 1.
An odd cubic Gaussian profile with two extrema and a stationary inflection
. Original function plot with the three stationary points marked. The near-zero cubic behavior explains the flat crossing without an extremum. Details.

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