Critical Points Calculator — Maxima & Minima
Use this free critical points calculator to find the critical points of a function on an interval and classify each as a local maximum, minimum, or saddle/inflection, with a graph and steps.
How it works
Critical points occur where the derivative is zero. The calculator locates each sign change of f′ on your interval, then uses the second derivative to classify it: f″ > 0 is a minimum, f″ < 0 is a maximum.
Original price was: $109.99.$54.99Current price is: $54.99.
How to use it
- Enter f(x) and the interval.
- Press Find critical points.
Related: the Derivative Calculator and the Tangent Line Calculator.
Frequently asked questions
What is a critical point?
A point where the derivative is zero (or undefined) — a candidate for a local maximum or minimum.
Original price was: $109.99.$54.99Current price is: $54.99.
How are they classified?
With the second derivative test: f″ > 0 means a local minimum, f″ < 0 a local maximum.
Original price was: $109.99.$54.99Current price is: $54.99.
Why an interval?
The tool searches numerically, so you give it a range of x to scan.
Original price was: $27.99.$17.99Current price is: $17.99.
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