Cubic Function - Derivative

Derivative

Through the quadratic formula the roots of the derivative f ′(x) = 3ax2 + 2bx + c are given by

and provide the critical points where the slope of the cubic function is zero. 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.

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