= Solution
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 $x=-1$, rises through the stationary <inflection point> at zero to its positive <maximum> at $x=1$, then decreases toward zero.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1-cubic-gaussian-profile.png]
{title=An odd cubic Gaussian profile with two extrema and a stationary inflection}
{description=Original function plot with the three stationary points marked. The near-zero cubic behavior explains the flat crossing without an extremum.}
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