Condition for No Distinct Stationary Points of a Cubic

Rarely Tested

Condition for No Distinct Stationary Points of a Cubic

For:

$$f(x)=ax^3+bx^2+cx+d$$

if:

$$b^2-3ac<0$$

then the cubic has no distinct real stationary points.

Usage

- Used to determine the monotonic nature of a cubic function.

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