Critical point of a cubic function ( local minimum )

Description

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of the cubic function is zero. They are found by setting derivative of the cubic equation equal to zero obtaining: f ′(x) = 3ax2 + 2bx + c = 0. The solutions of that equation are the critical points of the cubic equation. If b2 − 3ac > 0, then the cubic function has a local maximum and a local minimum. If b2 − 3ac = 0, then the cubic’s inflection point is the only critical point. If b2 − 3ac < 0, then there are no critical points. In the cases where b2 − 3ac ≤ 0, the cubic function is strictly monotonic.

Related formulas

Variables

xVariable (dimensionless)
bQuadratic coefficient (dimensionless)
aCubic coefficient (dimensionless)
cLinear coefficient (dimensionless)