What is the rule of cubic?

This behavior extends to all polynomials of odd degree, where the presence of real coefficients guarantees the existence of at least one real root. The cubic function, being a member of this class, adheres to this fundamental principle.

A cubic function, characterized by its real coefficients, possesses a unique property in its roots. Specifically, it can have either one real root, which may be a repeated one, or three distinct real roots.

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When graphed, a cubic function displays a distinctive curvature pattern. At the heart of this pattern lies a single inflection point, marking a change in the direction of concavity.

Besides its inflection point, the graph of a cubic function may also exhibit two critical points. These points represent local extrema, specifically a local minimum and a local maximum, where the function attains its smallest and largest values within a specific interval.