Critical Points Calculator (Cubic)
Find critical points of a cubic and classify them.
Enter your values
ⓘ Live results
Results
- Critical point 1
- x = 2 (local minimum)
- Critical point 2
- x = 0 (local maximum)
- f'(x)
- 3x^2 + -6x + 0
Quick answer
Critical points occur where f'(x)=0; the second derivative test classifies them as local maxima, minima or inconclusive.
f'(x)=3ax^2+2bx+c=0
How to use the Critical Points Calculator (Cubic)
- 1Enter the coefficients of a cubic polynomial.
- 2The derivative is set to zero and solved with the quadratic formula.
- 3The second derivative test classifies each critical point.
Worked example
Using the values the calculator loads with:
Inputs
- Coefficient of x^31
- Coefficient of x^2-3
- Coefficient of x0
- Constant2
Results
- Critical point 1x = 2 (local minimum)
- Critical point 2x = 0 (local maximum)
- f'(x)3x^2 + -6x + 0
Frequently asked questions
What if the discriminant is negative?
The derivative never crosses zero, so the cubic is monotonic with no local extrema.
What does 'inconclusive' mean?
The second derivative is also zero there, so a higher-order test or sign chart is needed.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.